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Simplifying (28 + x) * x = -146 Reorder the terms for easier multiplication: x(28 + x) = -146 (28 * x + x * x) = -146 (28x + x2) = -146 Solving 28x + x2 = -146 Solving for variable 'x'. Reorder the terms: 146 + 28x + x2 = -146 + 146 Combine like terms: -146 + 146 = 0 146 + 28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-146' to each side of the equation. 146 + 28x + -146 + x2 = 0 + -146 Reorder the terms: 146 + -146 + 28x + x2 = 0 + -146 Combine like terms: 146 + -146 = 0 0 + 28x + x2 = 0 + -146 28x + x2 = 0 + -146 Combine like terms: 0 + -146 = -146 28x + x2 = -146 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = -146 + 196 Reorder the terms: 196 + 28x + x2 = -146 + 196 Combine like terms: -146 + 196 = 50 196 + 28x + x2 = 50 Factor a perfect square on the left side: (x + 14)(x + 14) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + 14) equal to 7.071067812 and -7.071067812.Subproblem 1
x + 14 = 7.071067812 Simplifying x + 14 = 7.071067812 Reorder the terms: 14 + x = 7.071067812 Solving 14 + x = 7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 7.071067812 + -14 Combine like terms: 14 + -14 = 0 0 + x = 7.071067812 + -14 x = 7.071067812 + -14 Combine like terms: 7.071067812 + -14 = -6.928932188 x = -6.928932188 Simplifying x = -6.928932188Subproblem 2
x + 14 = -7.071067812 Simplifying x + 14 = -7.071067812 Reorder the terms: 14 + x = -7.071067812 Solving 14 + x = -7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -7.071067812 + -14 Combine like terms: 14 + -14 = 0 0 + x = -7.071067812 + -14 x = -7.071067812 + -14 Combine like terms: -7.071067812 + -14 = -21.071067812 x = -21.071067812 Simplifying x = -21.071067812Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.928932188, -21.071067812}
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