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Simplifying 324 = (x + 24) * x + 7 Reorder the terms: 324 = (24 + x) * x + 7 Reorder the terms for easier multiplication: 324 = x(24 + x) + 7 324 = (24 * x + x * x) + 7 324 = (24x + x2) + 7 Reorder the terms: 324 = 7 + 24x + x2 Solving 324 = 7 + 24x + x2 Solving for variable 'x'. Combine like terms: 324 + -7 = 317 317 + -24x + -1x2 = 7 + 24x + x2 + -7 + -24x + -1x2 Reorder the terms: 317 + -24x + -1x2 = 7 + -7 + 24x + -24x + x2 + -1x2 Combine like terms: 7 + -7 = 0 317 + -24x + -1x2 = 0 + 24x + -24x + x2 + -1x2 317 + -24x + -1x2 = 24x + -24x + x2 + -1x2 Combine like terms: 24x + -24x = 0 317 + -24x + -1x2 = 0 + x2 + -1x2 317 + -24x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 317 + -24x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -317 + 24x + x2 = 0 Move the constant term to the right: Add '317' to each side of the equation. -317 + 24x + 317 + x2 = 0 + 317 Reorder the terms: -317 + 317 + 24x + x2 = 0 + 317 Combine like terms: -317 + 317 = 0 0 + 24x + x2 = 0 + 317 24x + x2 = 0 + 317 Combine like terms: 0 + 317 = 317 24x + x2 = 317 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 317 + 144 Reorder the terms: 144 + 24x + x2 = 317 + 144 Combine like terms: 317 + 144 = 461 144 + 24x + x2 = 461 Factor a perfect square on the left side: (x + 12)(x + 12) = 461 Calculate the square root of the right side: 21.470910554 Break this problem into two subproblems by setting (x + 12) equal to 21.470910554 and -21.470910554.Subproblem 1
x + 12 = 21.470910554 Simplifying x + 12 = 21.470910554 Reorder the terms: 12 + x = 21.470910554 Solving 12 + x = 21.470910554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 21.470910554 + -12 Combine like terms: 12 + -12 = 0 0 + x = 21.470910554 + -12 x = 21.470910554 + -12 Combine like terms: 21.470910554 + -12 = 9.470910554 x = 9.470910554 Simplifying x = 9.470910554Subproblem 2
x + 12 = -21.470910554 Simplifying x + 12 = -21.470910554 Reorder the terms: 12 + x = -21.470910554 Solving 12 + x = -21.470910554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -21.470910554 + -12 Combine like terms: 12 + -12 = 0 0 + x = -21.470910554 + -12 x = -21.470910554 + -12 Combine like terms: -21.470910554 + -12 = -33.470910554 x = -33.470910554 Simplifying x = -33.470910554Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.470910554, -33.470910554}
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