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Simplifying x2 + 150x + -7900 = 0 Reorder the terms: -7900 + 150x + x2 = 0 Solving -7900 + 150x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7900' to each side of the equation. -7900 + 150x + 7900 + x2 = 0 + 7900 Reorder the terms: -7900 + 7900 + 150x + x2 = 0 + 7900 Combine like terms: -7900 + 7900 = 0 0 + 150x + x2 = 0 + 7900 150x + x2 = 0 + 7900 Combine like terms: 0 + 7900 = 7900 150x + x2 = 7900 The x term is 150x. Take half its coefficient (75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. 150x + 5625 + x2 = 7900 + 5625 Reorder the terms: 5625 + 150x + x2 = 7900 + 5625 Combine like terms: 7900 + 5625 = 13525 5625 + 150x + x2 = 13525 Factor a perfect square on the left side: (x + 75)(x + 75) = 13525 Calculate the square root of the right side: 116.297033496 Break this problem into two subproblems by setting (x + 75) equal to 116.297033496 and -116.297033496.Subproblem 1
x + 75 = 116.297033496 Simplifying x + 75 = 116.297033496 Reorder the terms: 75 + x = 116.297033496 Solving 75 + x = 116.297033496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = 116.297033496 + -75 Combine like terms: 75 + -75 = 0 0 + x = 116.297033496 + -75 x = 116.297033496 + -75 Combine like terms: 116.297033496 + -75 = 41.297033496 x = 41.297033496 Simplifying x = 41.297033496Subproblem 2
x + 75 = -116.297033496 Simplifying x + 75 = -116.297033496 Reorder the terms: 75 + x = -116.297033496 Solving 75 + x = -116.297033496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = -116.297033496 + -75 Combine like terms: 75 + -75 = 0 0 + x = -116.297033496 + -75 x = -116.297033496 + -75 Combine like terms: -116.297033496 + -75 = -191.297033496 x = -191.297033496 Simplifying x = -191.297033496Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.297033496, -191.297033496}
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