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Simplifying 8x + 4x(4x + -3) = 4(6x + 4) + -4 Reorder the terms: 8x + 4x(-3 + 4x) = 4(6x + 4) + -4 8x + (-3 * 4x + 4x * 4x) = 4(6x + 4) + -4 8x + (-12x + 16x2) = 4(6x + 4) + -4 Combine like terms: 8x + -12x = -4x -4x + 16x2 = 4(6x + 4) + -4 Reorder the terms: -4x + 16x2 = 4(4 + 6x) + -4 -4x + 16x2 = (4 * 4 + 6x * 4) + -4 -4x + 16x2 = (16 + 24x) + -4 Reorder the terms: -4x + 16x2 = 16 + -4 + 24x Combine like terms: 16 + -4 = 12 -4x + 16x2 = 12 + 24x Solving -4x + 16x2 = 12 + 24x Solving for variable 'x'. Reorder the terms: -12 + -4x + -24x + 16x2 = 12 + 24x + -12 + -24x Combine like terms: -4x + -24x = -28x -12 + -28x + 16x2 = 12 + 24x + -12 + -24x Reorder the terms: -12 + -28x + 16x2 = 12 + -12 + 24x + -24x Combine like terms: 12 + -12 = 0 -12 + -28x + 16x2 = 0 + 24x + -24x -12 + -28x + 16x2 = 24x + -24x Combine like terms: 24x + -24x = 0 -12 + -28x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + -7x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -7x + 4x2)' equal to zero and attempt to solve: Simplifying -3 + -7x + 4x2 = 0 Solving -3 + -7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + -1.75x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1.75x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1.75x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1.75x + x2 = 0 + 0.75 -1.75x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1.75x + x2 = 0.75 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = 0.75 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 0.75 + 0.765625 Combine like terms: 0.75 + 0.765625 = 1.515625 0.765625 + -1.75x + x2 = 1.515625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (x + -0.875) equal to 1.231107225 and -1.231107225.Subproblem 1
x + -0.875 = 1.231107225 Simplifying x + -0.875 = 1.231107225 Reorder the terms: -0.875 + x = 1.231107225 Solving -0.875 + x = 1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 1.231107225 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 1.231107225 + 0.875 x = 1.231107225 + 0.875 Combine like terms: 1.231107225 + 0.875 = 2.106107225 x = 2.106107225 Simplifying x = 2.106107225Subproblem 2
x + -0.875 = -1.231107225 Simplifying x + -0.875 = -1.231107225 Reorder the terms: -0.875 + x = -1.231107225 Solving -0.875 + x = -1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -1.231107225 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -1.231107225 + 0.875 x = -1.231107225 + 0.875 Combine like terms: -1.231107225 + 0.875 = -0.356107225 x = -0.356107225 Simplifying x = -0.356107225Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.106107225, -0.356107225}Solution
x = {2.106107225, -0.356107225}
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