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Simplifying x2 + -15x + -56 = 0 Reorder the terms: -56 + -15x + x2 = 0 Solving -56 + -15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -15x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + -15x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -15x + x2 = 0 + 56 -15x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 -15x + x2 = 56 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 = 56 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 56 + 56.25 Combine like terms: 56 + 56.25 = 112.25 56.25 + -15x + x2 = 112.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 112.25 Calculate the square root of the right side: 10.59481005 Break this problem into two subproblems by setting (x + -7.5) equal to 10.59481005 and -10.59481005.Subproblem 1
x + -7.5 = 10.59481005 Simplifying x + -7.5 = 10.59481005 Reorder the terms: -7.5 + x = 10.59481005 Solving -7.5 + x = 10.59481005 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 = 10.59481005 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 10.59481005 + 7.5 x = 10.59481005 + 7.5 Combine like terms: 10.59481005 + 7.5 = 18.09481005 x = 18.09481005 Simplifying x = 18.09481005Subproblem 2
x + -7.5 = -10.59481005 Simplifying x + -7.5 = -10.59481005 Reorder the terms: -7.5 + x = -10.59481005 Solving -7.5 + x = -10.59481005 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 = -10.59481005 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -10.59481005 + 7.5 x = -10.59481005 + 7.5 Combine like terms: -10.59481005 + 7.5 = -3.09481005 x = -3.09481005 Simplifying x = -3.09481005Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.09481005, -3.09481005}
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