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Simplifying (5x + -45)(x + -9) = 30 Reorder the terms: (-45 + 5x)(x + -9) = 30 Reorder the terms: (-45 + 5x)(-9 + x) = 30 Multiply (-45 + 5x) * (-9 + x) (-45(-9 + x) + 5x * (-9 + x)) = 30 ((-9 * -45 + x * -45) + 5x * (-9 + x)) = 30 ((405 + -45x) + 5x * (-9 + x)) = 30 (405 + -45x + (-9 * 5x + x * 5x)) = 30 (405 + -45x + (-45x + 5x2)) = 30 Combine like terms: -45x + -45x = -90x (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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