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Simplifying 297 = (x + 2)(x + 3) Reorder the terms: 297 = (2 + x)(x + 3) Reorder the terms: 297 = (2 + x)(3 + x) Multiply (2 + x) * (3 + x) 297 = (2(3 + x) + x(3 + x)) 297 = ((3 * 2 + x * 2) + x(3 + x)) 297 = ((6 + 2x) + x(3 + x)) 297 = (6 + 2x + (3 * x + x * x)) 297 = (6 + 2x + (3x + x2)) Combine like terms: 2x + 3x = 5x 297 = (6 + 5x + x2) Solving 297 = 6 + 5x + x2 Solving for variable 'x'. Combine like terms: 297 + -6 = 291 291 + -5x + -1x2 = 6 + 5x + x2 + -6 + -5x + -1x2 Reorder the terms: 291 + -5x + -1x2 = 6 + -6 + 5x + -5x + x2 + -1x2 Combine like terms: 6 + -6 = 0 291 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2 291 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 291 + -5x + -1x2 = 0 + x2 + -1x2 291 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 291 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -291 + 5x + x2 = 0 Move the constant term to the right: Add '291' to each side of the equation. -291 + 5x + 291 + x2 = 0 + 291 Reorder the terms: -291 + 291 + 5x + x2 = 0 + 291 Combine like terms: -291 + 291 = 0 0 + 5x + x2 = 0 + 291 5x + x2 = 0 + 291 Combine like terms: 0 + 291 = 291 5x + x2 = 291 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 291 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 291 + 6.25 Combine like terms: 291 + 6.25 = 297.25 6.25 + 5x + x2 = 297.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 297.25 Calculate the square root of the right side: 17.24093965 Break this problem into two subproblems by setting (x + 2.5) equal to 17.24093965 and -17.24093965.Subproblem 1
x + 2.5 = 17.24093965 Simplifying x + 2.5 = 17.24093965 Reorder the terms: 2.5 + x = 17.24093965 Solving 2.5 + x = 17.24093965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 17.24093965 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 17.24093965 + -2.5 x = 17.24093965 + -2.5 Combine like terms: 17.24093965 + -2.5 = 14.74093965 x = 14.74093965 Simplifying x = 14.74093965Subproblem 2
x + 2.5 = -17.24093965 Simplifying x + 2.5 = -17.24093965 Reorder the terms: 2.5 + x = -17.24093965 Solving 2.5 + x = -17.24093965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -17.24093965 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -17.24093965 + -2.5 x = -17.24093965 + -2.5 Combine like terms: -17.24093965 + -2.5 = -19.74093965 x = -19.74093965 Simplifying x = -19.74093965Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.74093965, -19.74093965}
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