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Simplifying 15x + -1x2 = 37 Solving 15x + -1x2 = 37 Solving for variable 'x'. Reorder the terms: -37 + 15x + -1x2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 37 + -15x + x2 = 0 Move the constant term to the right: Add '-37' to each side of the equation. 37 + -15x + -37 + x2 = 0 + -37 Reorder the terms: 37 + -37 + -15x + x2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + -15x + x2 = 0 + -37 -15x + x2 = 0 + -37 Combine like terms: 0 + -37 = -37 -15x + x2 = -37 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 = -37 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -37 + 56.25 Combine like terms: -37 + 56.25 = 19.25 56.25 + -15x + x2 = 19.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (x + -7.5) equal to 4.387482194 and -4.387482194.Subproblem 1
x + -7.5 = 4.387482194 Simplifying x + -7.5 = 4.387482194 Reorder the terms: -7.5 + x = 4.387482194 Solving -7.5 + x = 4.387482194 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 = 4.387482194 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 4.387482194 + 7.5 x = 4.387482194 + 7.5 Combine like terms: 4.387482194 + 7.5 = 11.887482194 x = 11.887482194 Simplifying x = 11.887482194Subproblem 2
x + -7.5 = -4.387482194 Simplifying x + -7.5 = -4.387482194 Reorder the terms: -7.5 + x = -4.387482194 Solving -7.5 + x = -4.387482194 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 = -4.387482194 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -4.387482194 + 7.5 x = -4.387482194 + 7.5 Combine like terms: -4.387482194 + 7.5 = 3.112517806 x = 3.112517806 Simplifying x = 3.112517806Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.887482194, 3.112517806}
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