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Simplifying 5(x + -3) + -9x = -2x(x + 17) Reorder the terms: 5(-3 + x) + -9x = -2x(x + 17) (-3 * 5 + x * 5) + -9x = -2x(x + 17) (-15 + 5x) + -9x = -2x(x + 17) Combine like terms: 5x + -9x = -4x -15 + -4x = -2x(x + 17) Reorder the terms: -15 + -4x = -2x(17 + x) -15 + -4x = (17 * -2x + x * -2x) -15 + -4x = (-34x + -2x2) Solving -15 + -4x = -34x + -2x2 Solving for variable 'x'. Combine like terms: -4x + 34x = 30x -15 + 30x + 2x2 = -34x + -2x2 + 34x + 2x2 Reorder the terms: -15 + 30x + 2x2 = -34x + 34x + -2x2 + 2x2 Combine like terms: -34x + 34x = 0 -15 + 30x + 2x2 = 0 + -2x2 + 2x2 -15 + 30x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -15 + 30x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + 15x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 15x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 15x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 15x + x2 = 0 + 7.5 15x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 15x + x2 = 7.5 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 = 7.5 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 7.5 + 56.25 Combine like terms: 7.5 + 56.25 = 63.75 56.25 + 15x + x2 = 63.75 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 63.75 Calculate the square root of the right side: 7.984359711 Break this problem into two subproblems by setting (x + 7.5) equal to 7.984359711 and -7.984359711.Subproblem 1
x + 7.5 = 7.984359711 Simplifying x + 7.5 = 7.984359711 Reorder the terms: 7.5 + x = 7.984359711 Solving 7.5 + x = 7.984359711 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 = 7.984359711 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 7.984359711 + -7.5 x = 7.984359711 + -7.5 Combine like terms: 7.984359711 + -7.5 = 0.484359711 x = 0.484359711 Simplifying x = 0.484359711Subproblem 2
x + 7.5 = -7.984359711 Simplifying x + 7.5 = -7.984359711 Reorder the terms: 7.5 + x = -7.984359711 Solving 7.5 + x = -7.984359711 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 = -7.984359711 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -7.984359711 + -7.5 x = -7.984359711 + -7.5 Combine like terms: -7.984359711 + -7.5 = -15.484359711 x = -15.484359711 Simplifying x = -15.484359711Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.484359711, -15.484359711}
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