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Simplifying -25(4x + -3)(4x + -3) = -5(3x + -2) Reorder the terms: -25(-3 + 4x)(4x + -3) = -5(3x + -2) Reorder the terms: -25(-3 + 4x)(-3 + 4x) = -5(3x + -2) Multiply (-3 + 4x) * (-3 + 4x) -25(-3(-3 + 4x) + 4x * (-3 + 4x)) = -5(3x + -2) -25((-3 * -3 + 4x * -3) + 4x * (-3 + 4x)) = -5(3x + -2) -25((9 + -12x) + 4x * (-3 + 4x)) = -5(3x + -2) -25(9 + -12x + (-3 * 4x + 4x * 4x)) = -5(3x + -2) -25(9 + -12x + (-12x + 16x2)) = -5(3x + -2) Combine like terms: -12x + -12x = -24x -25(9 + -24x + 16x2) = -5(3x + -2) (9 * -25 + -24x * -25 + 16x2 * -25) = -5(3x + -2) (-225 + 600x + -400x2) = -5(3x + -2) Reorder the terms: -225 + 600x + -400x2 = -5(-2 + 3x) -225 + 600x + -400x2 = (-2 * -5 + 3x * -5) -225 + 600x + -400x2 = (10 + -15x) Solving -225 + 600x + -400x2 = 10 + -15x Solving for variable 'x'. Reorder the terms: -225 + -10 + 600x + 15x + -400x2 = 10 + -15x + -10 + 15x Combine like terms: -225 + -10 = -235 -235 + 600x + 15x + -400x2 = 10 + -15x + -10 + 15x Combine like terms: 600x + 15x = 615x -235 + 615x + -400x2 = 10 + -15x + -10 + 15x Reorder the terms: -235 + 615x + -400x2 = 10 + -10 + -15x + 15x Combine like terms: 10 + -10 = 0 -235 + 615x + -400x2 = 0 + -15x + 15x -235 + 615x + -400x2 = -15x + 15x Combine like terms: -15x + 15x = 0 -235 + 615x + -400x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-47 + 123x + -80x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-47 + 123x + -80x2)' equal to zero and attempt to solve: Simplifying -47 + 123x + -80x2 = 0 Solving -47 + 123x + -80x2 = 0 Begin completing the square. Divide all terms by -80 the coefficient of the squared term: Divide each side by '-80'. 0.5875 + -1.5375x + x2 = 0.0 Move the constant term to the right: Add '-0.5875' to each side of the equation. 0.5875 + -1.5375x + -0.5875 + x2 = 0.0 + -0.5875 Reorder the terms: 0.5875 + -0.5875 + -1.5375x + x2 = 0.0 + -0.5875 Combine like terms: 0.5875 + -0.5875 = 0.0000 0.0000 + -1.5375x + x2 = 0.0 + -0.5875 -1.5375x + x2 = 0.0 + -0.5875 Combine like terms: 0.0 + -0.5875 = -0.5875 -1.5375x + x2 = -0.5875 The x term is -1.5375x. Take half its coefficient (-0.76875). Square it (0.5909765625) and add it to both sides. Add '0.5909765625' to each side of the equation. -1.5375x + 0.5909765625 + x2 = -0.5875 + 0.5909765625 Reorder the terms: 0.5909765625 + -1.5375x + x2 = -0.5875 + 0.5909765625 Combine like terms: -0.5875 + 0.5909765625 = 0.0034765625 0.5909765625 + -1.5375x + x2 = 0.0034765625 Factor a perfect square on the left side: (x + -0.76875)(x + -0.76875) = 0.0034765625 Calculate the square root of the right side: 0.058962382 Break this problem into two subproblems by setting (x + -0.76875) equal to 0.058962382 and -0.058962382.Subproblem 1
x + -0.76875 = 0.058962382 Simplifying x + -0.76875 = 0.058962382 Reorder the terms: -0.76875 + x = 0.058962382 Solving -0.76875 + x = 0.058962382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.76875' to each side of the equation. -0.76875 + 0.76875 + x = 0.058962382 + 0.76875 Combine like terms: -0.76875 + 0.76875 = 0.00000 0.00000 + x = 0.058962382 + 0.76875 x = 0.058962382 + 0.76875 Combine like terms: 0.058962382 + 0.76875 = 0.827712382 x = 0.827712382 Simplifying x = 0.827712382Subproblem 2
x + -0.76875 = -0.058962382 Simplifying x + -0.76875 = -0.058962382 Reorder the terms: -0.76875 + x = -0.058962382 Solving -0.76875 + x = -0.058962382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.76875' to each side of the equation. -0.76875 + 0.76875 + x = -0.058962382 + 0.76875 Combine like terms: -0.76875 + 0.76875 = 0.00000 0.00000 + x = -0.058962382 + 0.76875 x = -0.058962382 + 0.76875 Combine like terms: -0.058962382 + 0.76875 = 0.709787618 x = 0.709787618 Simplifying x = 0.709787618Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.827712382, 0.709787618}Solution
x = {0.827712382, 0.709787618}
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