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Simplifying 5[(x + -9)(x + -9)] = 30 Reorder the terms: 5[(-9 + x)(x + -9)] = 30 Reorder the terms: 5[(-9 + x)(-9 + x)] = 30 Multiply (-9 + x) * (-9 + x) 5[(-9(-9 + x) + x(-9 + x))] = 30 5[((-9 * -9 + x * -9) + x(-9 + x))] = 30 5[((81 + -9x) + x(-9 + x))] = 30 5[(81 + -9x + (-9 * x + x * x))] = 30 5[(81 + -9x + (-9x + x2))] = 30 Combine like terms: -9x + -9x = -18x 5[(81 + -18x + x2)] = 30 [81 * 5 + -18x * 5 + x2 * 5] = 30 [405 + -90x + 5x2] = 30 Solving 405 + -90x + 5x2 = 30 Solving for variable 'x'. Reorder the terms: 405 + -30 + -90x + 5x2 = 30 + -30 Combine like terms: 405 + -30 = 375 375 + -90x + 5x2 = 30 + -30 Combine like terms: 30 + -30 = 0 375 + -90x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(75 + -18x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(75 + -18x + x2)' equal to zero and attempt to solve: Simplifying 75 + -18x + x2 = 0 Solving 75 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-75' to each side of the equation. 75 + -18x + -75 + x2 = 0 + -75 Reorder the terms: 75 + -75 + -18x + x2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -18x + x2 = 0 + -75 -18x + x2 = 0 + -75 Combine like terms: 0 + -75 = -75 -18x + x2 = -75 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 = -75 + 81 Reorder the terms: 81 + -18x + x2 = -75 + 81 Combine like terms: -75 + 81 = 6 81 + -18x + x2 = 6 Factor a perfect square on the left side: (x + -9)(x + -9) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -9) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -9 = 2.449489743 Simplifying x + -9 = 2.449489743 Reorder the terms: -9 + x = 2.449489743 Solving -9 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 2.449489743 + 9 Combine like terms: -9 + 9 = 0 0 + x = 2.449489743 + 9 x = 2.449489743 + 9 Combine like terms: 2.449489743 + 9 = 11.449489743 x = 11.449489743 Simplifying x = 11.449489743Subproblem 2
x + -9 = -2.449489743 Simplifying x + -9 = -2.449489743 Reorder the terms: -9 + x = -2.449489743 Solving -9 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -2.449489743 + 9 Combine like terms: -9 + 9 = 0 0 + x = -2.449489743 + 9 x = -2.449489743 + 9 Combine like terms: -2.449489743 + 9 = 6.550510257 x = 6.550510257 Simplifying x = 6.550510257Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.449489743, 6.550510257}Solution
x = {11.449489743, 6.550510257}
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