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Simplifying 122 + 15x = x(72 + -5x) 122 + 15x = (72 * x + -5x * x) 122 + 15x = (72x + -5x2) Solving 122 + 15x = 72x + -5x2 Solving for variable 'x'. Combine like terms: 15x + -72x = -57x 122 + -57x + 5x2 = 72x + -5x2 + -72x + 5x2 Reorder the terms: 122 + -57x + 5x2 = 72x + -72x + -5x2 + 5x2 Combine like terms: 72x + -72x = 0 122 + -57x + 5x2 = 0 + -5x2 + 5x2 122 + -57x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 122 + -57x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 24.4 + -11.4x + x2 = 0 Move the constant term to the right: Add '-24.4' to each side of the equation. 24.4 + -11.4x + -24.4 + x2 = 0 + -24.4 Reorder the terms: 24.4 + -24.4 + -11.4x + x2 = 0 + -24.4 Combine like terms: 24.4 + -24.4 = 0.0 0.0 + -11.4x + x2 = 0 + -24.4 -11.4x + x2 = 0 + -24.4 Combine like terms: 0 + -24.4 = -24.4 -11.4x + x2 = -24.4 The x term is -11.4x. Take half its coefficient (-5.7). Square it (32.49) and add it to both sides. Add '32.49' to each side of the equation. -11.4x + 32.49 + x2 = -24.4 + 32.49 Reorder the terms: 32.49 + -11.4x + x2 = -24.4 + 32.49 Combine like terms: -24.4 + 32.49 = 8.09 32.49 + -11.4x + x2 = 8.09 Factor a perfect square on the left side: (x + -5.7)(x + -5.7) = 8.09 Calculate the square root of the right side: 2.844292531 Break this problem into two subproblems by setting (x + -5.7) equal to 2.844292531 and -2.844292531.Subproblem 1
x + -5.7 = 2.844292531 Simplifying x + -5.7 = 2.844292531 Reorder the terms: -5.7 + x = 2.844292531 Solving -5.7 + x = 2.844292531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.7' to each side of the equation. -5.7 + 5.7 + x = 2.844292531 + 5.7 Combine like terms: -5.7 + 5.7 = 0.0 0.0 + x = 2.844292531 + 5.7 x = 2.844292531 + 5.7 Combine like terms: 2.844292531 + 5.7 = 8.544292531 x = 8.544292531 Simplifying x = 8.544292531Subproblem 2
x + -5.7 = -2.844292531 Simplifying x + -5.7 = -2.844292531 Reorder the terms: -5.7 + x = -2.844292531 Solving -5.7 + x = -2.844292531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.7' to each side of the equation. -5.7 + 5.7 + x = -2.844292531 + 5.7 Combine like terms: -5.7 + 5.7 = 0.0 0.0 + x = -2.844292531 + 5.7 x = -2.844292531 + 5.7 Combine like terms: -2.844292531 + 5.7 = 2.855707469 x = 2.855707469 Simplifying x = 2.855707469Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.544292531, 2.855707469}
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