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Simplifying x2 + -15x + -91 = 0 Reorder the terms: -91 + -15x + x2 = 0 Solving -91 + -15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '91' to each side of the equation. -91 + -15x + 91 + x2 = 0 + 91 Reorder the terms: -91 + 91 + -15x + x2 = 0 + 91 Combine like terms: -91 + 91 = 0 0 + -15x + x2 = 0 + 91 -15x + x2 = 0 + 91 Combine like terms: 0 + 91 = 91 -15x + x2 = 91 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 = 91 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 91 + 56.25 Combine like terms: 91 + 56.25 = 147.25 56.25 + -15x + x2 = 147.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 147.25 Calculate the square root of the right side: 12.1346611 Break this problem into two subproblems by setting (x + -7.5) equal to 12.1346611 and -12.1346611.Subproblem 1
x + -7.5 = 12.1346611 Simplifying x + -7.5 = 12.1346611 Reorder the terms: -7.5 + x = 12.1346611 Solving -7.5 + x = 12.1346611 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 = 12.1346611 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 12.1346611 + 7.5 x = 12.1346611 + 7.5 Combine like terms: 12.1346611 + 7.5 = 19.6346611 x = 19.6346611 Simplifying x = 19.6346611Subproblem 2
x + -7.5 = -12.1346611 Simplifying x + -7.5 = -12.1346611 Reorder the terms: -7.5 + x = -12.1346611 Solving -7.5 + x = -12.1346611 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 = -12.1346611 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -12.1346611 + 7.5 x = -12.1346611 + 7.5 Combine like terms: -12.1346611 + 7.5 = -4.6346611 x = -4.6346611 Simplifying x = -4.6346611Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.6346611, -4.6346611}
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