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Simplifying 0 = -16(x2 + -15x + -1) Reorder the terms: 0 = -16(-1 + -15x + x2) 0 = (-1 * -16 + -15x * -16 + x2 * -16) 0 = (16 + 240x + -16x2) Solving 0 = 16 + 240x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -16 = -16 -16 + -240x + 16x2 = 16 + 240x + -16x2 + -16 + -240x + 16x2 Reorder the terms: -16 + -240x + 16x2 = 16 + -16 + 240x + -240x + -16x2 + 16x2 Combine like terms: 16 + -16 = 0 -16 + -240x + 16x2 = 0 + 240x + -240x + -16x2 + 16x2 -16 + -240x + 16x2 = 240x + -240x + -16x2 + 16x2 Combine like terms: 240x + -240x = 0 -16 + -240x + 16x2 = 0 + -16x2 + 16x2 -16 + -240x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -16 + -240x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-1 + -15x + x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-1 + -15x + x2)' equal to zero and attempt to solve: Simplifying -1 + -15x + x2 = 0 Solving -1 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -15x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -15x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -15x + x2 = 0 + 1 -15x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -15x + x2 = 1 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 = 1 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 1 + 56.25 Combine like terms: 1 + 56.25 = 57.25 56.25 + -15x + x2 = 57.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 57.25 Calculate the square root of the right side: 7.566372975 Break this problem into two subproblems by setting (x + -7.5) equal to 7.566372975 and -7.566372975.Subproblem 1
x + -7.5 = 7.566372975 Simplifying x + -7.5 = 7.566372975 Reorder the terms: -7.5 + x = 7.566372975 Solving -7.5 + x = 7.566372975 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 = 7.566372975 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.566372975 + 7.5 x = 7.566372975 + 7.5 Combine like terms: 7.566372975 + 7.5 = 15.066372975 x = 15.066372975 Simplifying x = 15.066372975Subproblem 2
x + -7.5 = -7.566372975 Simplifying x + -7.5 = -7.566372975 Reorder the terms: -7.5 + x = -7.566372975 Solving -7.5 + x = -7.566372975 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 = -7.566372975 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.566372975 + 7.5 x = -7.566372975 + 7.5 Combine like terms: -7.566372975 + 7.5 = -0.066372975 x = -0.066372975 Simplifying x = -0.066372975Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.066372975, -0.066372975}Solution
x = {15.066372975, -0.066372975}
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