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Simplifying -1x2 + 15x + -34 = 0 Reorder the terms: -34 + 15x + -1x2 = 0 Solving -34 + 15x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 34 + -15x + x2 = 0 Move the constant term to the right: Add '-34' to each side of the equation. 34 + -15x + -34 + x2 = 0 + -34 Reorder the terms: 34 + -34 + -15x + x2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -15x + x2 = 0 + -34 -15x + x2 = 0 + -34 Combine like terms: 0 + -34 = -34 -15x + x2 = -34 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 = -34 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -34 + 56.25 Combine like terms: -34 + 56.25 = 22.25 56.25 + -15x + x2 = 22.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x + -7.5) equal to 4.716990566 and -4.716990566.Subproblem 1
x + -7.5 = 4.716990566 Simplifying x + -7.5 = 4.716990566 Reorder the terms: -7.5 + x = 4.716990566 Solving -7.5 + x = 4.716990566 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 = 4.716990566 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 4.716990566 + 7.5 x = 4.716990566 + 7.5 Combine like terms: 4.716990566 + 7.5 = 12.216990566 x = 12.216990566 Simplifying x = 12.216990566Subproblem 2
x + -7.5 = -4.716990566 Simplifying x + -7.5 = -4.716990566 Reorder the terms: -7.5 + x = -4.716990566 Solving -7.5 + x = -4.716990566 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 = -4.716990566 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -4.716990566 + 7.5 x = -4.716990566 + 7.5 Combine like terms: -4.716990566 + 7.5 = 2.783009434 x = 2.783009434 Simplifying x = 2.783009434Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.216990566, 2.783009434}
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