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Simplifying 5(x + -2) + -7(x + 1) = 9x(3 + -2x) Reorder the terms: 5(-2 + x) + -7(x + 1) = 9x(3 + -2x) (-2 * 5 + x * 5) + -7(x + 1) = 9x(3 + -2x) (-10 + 5x) + -7(x + 1) = 9x(3 + -2x) Reorder the terms: -10 + 5x + -7(1 + x) = 9x(3 + -2x) -10 + 5x + (1 * -7 + x * -7) = 9x(3 + -2x) -10 + 5x + (-7 + -7x) = 9x(3 + -2x) Reorder the terms: -10 + -7 + 5x + -7x = 9x(3 + -2x) Combine like terms: -10 + -7 = -17 -17 + 5x + -7x = 9x(3 + -2x) Combine like terms: 5x + -7x = -2x -17 + -2x = 9x(3 + -2x) -17 + -2x = (3 * 9x + -2x * 9x) -17 + -2x = (27x + -18x2) Solving -17 + -2x = 27x + -18x2 Solving for variable 'x'. Combine like terms: -2x + -27x = -29x -17 + -29x + 18x2 = 27x + -18x2 + -27x + 18x2 Reorder the terms: -17 + -29x + 18x2 = 27x + -27x + -18x2 + 18x2 Combine like terms: 27x + -27x = 0 -17 + -29x + 18x2 = 0 + -18x2 + 18x2 -17 + -29x + 18x2 = -18x2 + 18x2 Combine like terms: -18x2 + 18x2 = 0 -17 + -29x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.9444444444 + -1.611111111x + x2 = 0 Move the constant term to the right: Add '0.9444444444' to each side of the equation. -0.9444444444 + -1.611111111x + 0.9444444444 + x2 = 0 + 0.9444444444 Reorder the terms: -0.9444444444 + 0.9444444444 + -1.611111111x + x2 = 0 + 0.9444444444 Combine like terms: -0.9444444444 + 0.9444444444 = 0.0000000000 0.0000000000 + -1.611111111x + x2 = 0 + 0.9444444444 -1.611111111x + x2 = 0 + 0.9444444444 Combine like terms: 0 + 0.9444444444 = 0.9444444444 -1.611111111x + x2 = 0.9444444444 The x term is -1.611111111x. Take half its coefficient (-0.8055555555). Square it (0.6489197530) and add it to both sides. Add '0.6489197530' to each side of the equation. -1.611111111x + 0.6489197530 + x2 = 0.9444444444 + 0.6489197530 Reorder the terms: 0.6489197530 + -1.611111111x + x2 = 0.9444444444 + 0.6489197530 Combine like terms: 0.9444444444 + 0.6489197530 = 1.5933641974 0.6489197530 + -1.611111111x + x2 = 1.5933641974 Factor a perfect square on the left side: (x + -0.8055555555)(x + -0.8055555555) = 1.5933641974 Calculate the square root of the right side: 1.262285307 Break this problem into two subproblems by setting (x + -0.8055555555) equal to 1.262285307 and -1.262285307.Subproblem 1
x + -0.8055555555 = 1.262285307 Simplifying x + -0.8055555555 = 1.262285307 Reorder the terms: -0.8055555555 + x = 1.262285307 Solving -0.8055555555 + x = 1.262285307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8055555555' to each side of the equation. -0.8055555555 + 0.8055555555 + x = 1.262285307 + 0.8055555555 Combine like terms: -0.8055555555 + 0.8055555555 = 0.0000000000 0.0000000000 + x = 1.262285307 + 0.8055555555 x = 1.262285307 + 0.8055555555 Combine like terms: 1.262285307 + 0.8055555555 = 2.0678408625 x = 2.0678408625 Simplifying x = 2.0678408625Subproblem 2
x + -0.8055555555 = -1.262285307 Simplifying x + -0.8055555555 = -1.262285307 Reorder the terms: -0.8055555555 + x = -1.262285307 Solving -0.8055555555 + x = -1.262285307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8055555555' to each side of the equation. -0.8055555555 + 0.8055555555 + x = -1.262285307 + 0.8055555555 Combine like terms: -0.8055555555 + 0.8055555555 = 0.0000000000 0.0000000000 + x = -1.262285307 + 0.8055555555 x = -1.262285307 + 0.8055555555 Combine like terms: -1.262285307 + 0.8055555555 = -0.4567297515 x = -0.4567297515 Simplifying x = -0.4567297515Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0678408625, -0.4567297515}
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