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Simplifying 7((x + 9)(x + 9)) + 126 = 0 Reorder the terms: 7((9 + x)(x + 9)) + 126 = 0 Reorder the terms: 7((9 + x)(9 + x)) + 126 = 0 Multiply (9 + x) * (9 + x) 7((9(9 + x) + x(9 + x))) + 126 = 0 7(((9 * 9 + x * 9) + x(9 + x))) + 126 = 0 7(((81 + 9x) + x(9 + x))) + 126 = 0 7((81 + 9x + (9 * x + x * x))) + 126 = 0 7((81 + 9x + (9x + x2))) + 126 = 0 Combine like terms: 9x + 9x = 18x 7((81 + 18x + x2)) + 126 = 0 (81 * 7 + 18x * 7 + x2 * 7) + 126 = 0 (567 + 126x + 7x2) + 126 = 0 Reorder the terms: 567 + 126 + 126x + 7x2 = 0 Combine like terms: 567 + 126 = 693 693 + 126x + 7x2 = 0 Solving 693 + 126x + 7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(99 + 18x + x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(99 + 18x + x2)' equal to zero and attempt to solve: Simplifying 99 + 18x + x2 = 0 Solving 99 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-99' to each side of the equation. 99 + 18x + -99 + x2 = 0 + -99 Reorder the terms: 99 + -99 + 18x + x2 = 0 + -99 Combine like terms: 99 + -99 = 0 0 + 18x + x2 = 0 + -99 18x + x2 = 0 + -99 Combine like terms: 0 + -99 = -99 18x + x2 = -99 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -99 + 81 Reorder the terms: 81 + 18x + x2 = -99 + 81 Combine like terms: -99 + 81 = -18 81 + 18x + x2 = -18 Factor a perfect square on the left side: (x + 9)(x + 9) = -18 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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