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Simplifying 5x(2x + 1) + -3x = 8(x + 5) Reorder the terms: 5x(1 + 2x) + -3x = 8(x + 5) (1 * 5x + 2x * 5x) + -3x = 8(x + 5) (5x + 10x2) + -3x = 8(x + 5) Reorder the terms: 5x + -3x + 10x2 = 8(x + 5) Combine like terms: 5x + -3x = 2x 2x + 10x2 = 8(x + 5) Reorder the terms: 2x + 10x2 = 8(5 + x) 2x + 10x2 = (5 * 8 + x * 8) 2x + 10x2 = (40 + 8x) Solving 2x + 10x2 = 40 + 8x Solving for variable 'x'. Reorder the terms: -40 + 2x + -8x + 10x2 = 40 + 8x + -40 + -8x Combine like terms: 2x + -8x = -6x -40 + -6x + 10x2 = 40 + 8x + -40 + -8x Reorder the terms: -40 + -6x + 10x2 = 40 + -40 + 8x + -8x Combine like terms: 40 + -40 = 0 -40 + -6x + 10x2 = 0 + 8x + -8x -40 + -6x + 10x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -40 + -6x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + -3x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-20 + -3x + 5x2)' equal to zero and attempt to solve: Simplifying -20 + -3x + 5x2 = 0 Solving -20 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + -0.6x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.6x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -0.6x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.6x + x2 = 0 + 4 -0.6x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.6x + x2 = 4 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 4 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 4 + 0.09 Combine like terms: 4 + 0.09 = 4.09 0.09 + -0.6x + x2 = 4.09 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 4.09 Calculate the square root of the right side: 2.022374842 Break this problem into two subproblems by setting (x + -0.3) equal to 2.022374842 and -2.022374842.Subproblem 1
x + -0.3 = 2.022374842 Simplifying x + -0.3 = 2.022374842 Reorder the terms: -0.3 + x = 2.022374842 Solving -0.3 + x = 2.022374842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 2.022374842 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 2.022374842 + 0.3 x = 2.022374842 + 0.3 Combine like terms: 2.022374842 + 0.3 = 2.322374842 x = 2.322374842 Simplifying x = 2.322374842Subproblem 2
x + -0.3 = -2.022374842 Simplifying x + -0.3 = -2.022374842 Reorder the terms: -0.3 + x = -2.022374842 Solving -0.3 + x = -2.022374842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -2.022374842 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -2.022374842 + 0.3 x = -2.022374842 + 0.3 Combine like terms: -2.022374842 + 0.3 = -1.722374842 x = -1.722374842 Simplifying x = -1.722374842Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.322374842, -1.722374842}Solution
x = {2.322374842, -1.722374842}
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