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Simplifying (4x)(x + -15) = 45 Remove parenthesis around (4x) 4x(x + -15) = 45 Reorder the terms: 4x(-15 + x) = 45 (-15 * 4x + x * 4x) = 45 (-60x + 4x2) = 45 Solving -60x + 4x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + -60x + 4x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + -60x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -11.25 + -15x + x2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + -15x + 11.25 + x2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + -15x + x2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + -15x + x2 = 0 + 11.25 -15x + x2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 -15x + x2 = 11.25 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 11.25 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 11.25 + 56.25 Combine like terms: 11.25 + 56.25 = 67.5 56.25 + -15x + x2 = 67.5 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 67.5 Calculate the square root of the right side: 8.215838363 Break this problem into two subproblems by setting (x + -7.5) equal to 8.215838363 and -8.215838363.Subproblem 1
x + -7.5 = 8.215838363 Simplifying x + -7.5 = 8.215838363 Reorder the terms: -7.5 + x = 8.215838363 Solving -7.5 + x = 8.215838363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 8.215838363 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 8.215838363 + 7.5 x = 8.215838363 + 7.5 Combine like terms: 8.215838363 + 7.5 = 15.715838363 x = 15.715838363 Simplifying x = 15.715838363Subproblem 2
x + -7.5 = -8.215838363 Simplifying x + -7.5 = -8.215838363 Reorder the terms: -7.5 + x = -8.215838363 Solving -7.5 + x = -8.215838363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -8.215838363 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -8.215838363 + 7.5 x = -8.215838363 + 7.5 Combine like terms: -8.215838363 + 7.5 = -0.715838363 x = -0.715838363 Simplifying x = -0.715838363Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.715838363, -0.715838363}
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