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Simplifying -9x + 15 = -22 + -4x(x + 12) Reorder the terms: 15 + -9x = -22 + -4x(x + 12) Reorder the terms: 15 + -9x = -22 + -4x(12 + x) 15 + -9x = -22 + (12 * -4x + x * -4x) 15 + -9x = -22 + (-48x + -4x2) Solving 15 + -9x = -22 + -48x + -4x2 Solving for variable 'x'. Reorder the terms: 15 + 22 + -9x + 48x + 4x2 = -22 + -48x + -4x2 + 22 + 48x + 4x2 Combine like terms: 15 + 22 = 37 37 + -9x + 48x + 4x2 = -22 + -48x + -4x2 + 22 + 48x + 4x2 Combine like terms: -9x + 48x = 39x 37 + 39x + 4x2 = -22 + -48x + -4x2 + 22 + 48x + 4x2 Reorder the terms: 37 + 39x + 4x2 = -22 + 22 + -48x + 48x + -4x2 + 4x2 Combine like terms: -22 + 22 = 0 37 + 39x + 4x2 = 0 + -48x + 48x + -4x2 + 4x2 37 + 39x + 4x2 = -48x + 48x + -4x2 + 4x2 Combine like terms: -48x + 48x = 0 37 + 39x + 4x2 = 0 + -4x2 + 4x2 37 + 39x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 37 + 39x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 9.25 + 9.75x + x2 = 0 Move the constant term to the right: Add '-9.25' to each side of the equation. 9.25 + 9.75x + -9.25 + x2 = 0 + -9.25 Reorder the terms: 9.25 + -9.25 + 9.75x + x2 = 0 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + 9.75x + x2 = 0 + -9.25 9.75x + x2 = 0 + -9.25 Combine like terms: 0 + -9.25 = -9.25 9.75x + x2 = -9.25 The x term is 9.75x. Take half its coefficient (4.875). Square it (23.765625) and add it to both sides. Add '23.765625' to each side of the equation. 9.75x + 23.765625 + x2 = -9.25 + 23.765625 Reorder the terms: 23.765625 + 9.75x + x2 = -9.25 + 23.765625 Combine like terms: -9.25 + 23.765625 = 14.515625 23.765625 + 9.75x + x2 = 14.515625 Factor a perfect square on the left side: (x + 4.875)(x + 4.875) = 14.515625 Calculate the square root of the right side: 3.809937664 Break this problem into two subproblems by setting (x + 4.875) equal to 3.809937664 and -3.809937664.Subproblem 1
x + 4.875 = 3.809937664 Simplifying x + 4.875 = 3.809937664 Reorder the terms: 4.875 + x = 3.809937664 Solving 4.875 + x = 3.809937664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.875' to each side of the equation. 4.875 + -4.875 + x = 3.809937664 + -4.875 Combine like terms: 4.875 + -4.875 = 0.000 0.000 + x = 3.809937664 + -4.875 x = 3.809937664 + -4.875 Combine like terms: 3.809937664 + -4.875 = -1.065062336 x = -1.065062336 Simplifying x = -1.065062336Subproblem 2
x + 4.875 = -3.809937664 Simplifying x + 4.875 = -3.809937664 Reorder the terms: 4.875 + x = -3.809937664 Solving 4.875 + x = -3.809937664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.875' to each side of the equation. 4.875 + -4.875 + x = -3.809937664 + -4.875 Combine like terms: 4.875 + -4.875 = 0.000 0.000 + x = -3.809937664 + -4.875 x = -3.809937664 + -4.875 Combine like terms: -3.809937664 + -4.875 = -8.684937664 x = -8.684937664 Simplifying x = -8.684937664Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.065062336, -8.684937664}
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