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Simplifying 5((x + -9)(x + -9)) = 3 Reorder the terms: 5((-9 + x)(x + -9)) = 3 Reorder the terms: 5((-9 + x)(-9 + x)) = 3 Multiply (-9 + x) * (-9 + x) 5((-9(-9 + x) + x(-9 + x))) = 3 5(((-9 * -9 + x * -9) + x(-9 + x))) = 3 5(((81 + -9x) + x(-9 + x))) = 3 5((81 + -9x + (-9 * x + x * x))) = 3 5((81 + -9x + (-9x + x2))) = 3 Combine like terms: -9x + -9x = -18x 5((81 + -18x + x2)) = 3 (81 * 5 + -18x * 5 + x2 * 5) = 3 (405 + -90x + 5x2) = 3 Solving 405 + -90x + 5x2 = 3 Solving for variable 'x'. Reorder the terms: 405 + -3 + -90x + 5x2 = 3 + -3 Combine like terms: 405 + -3 = 402 402 + -90x + 5x2 = 3 + -3 Combine like terms: 3 + -3 = 0 402 + -90x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 80.4 + -18x + x2 = 0 Move the constant term to the right: Add '-80.4' to each side of the equation. 80.4 + -18x + -80.4 + x2 = 0 + -80.4 Reorder the terms: 80.4 + -80.4 + -18x + x2 = 0 + -80.4 Combine like terms: 80.4 + -80.4 = 0.0 0.0 + -18x + x2 = 0 + -80.4 -18x + x2 = 0 + -80.4 Combine like terms: 0 + -80.4 = -80.4 -18x + x2 = -80.4 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 = -80.4 + 81 Reorder the terms: 81 + -18x + x2 = -80.4 + 81 Combine like terms: -80.4 + 81 = 0.6 81 + -18x + x2 = 0.6 Factor a perfect square on the left side: (x + -9)(x + -9) = 0.6 Calculate the square root of the right side: 0.774596669 Break this problem into two subproblems by setting (x + -9) equal to 0.774596669 and -0.774596669.Subproblem 1
x + -9 = 0.774596669 Simplifying x + -9 = 0.774596669 Reorder the terms: -9 + x = 0.774596669 Solving -9 + x = 0.774596669 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 = 0.774596669 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0.774596669 + 9 x = 0.774596669 + 9 Combine like terms: 0.774596669 + 9 = 9.774596669 x = 9.774596669 Simplifying x = 9.774596669Subproblem 2
x + -9 = -0.774596669 Simplifying x + -9 = -0.774596669 Reorder the terms: -9 + x = -0.774596669 Solving -9 + x = -0.774596669 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 = -0.774596669 + 9 Combine like terms: -9 + 9 = 0 0 + x = -0.774596669 + 9 x = -0.774596669 + 9 Combine like terms: -0.774596669 + 9 = 8.225403331 x = 8.225403331 Simplifying x = 8.225403331Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.774596669, 8.225403331}
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