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Simplifying 10(x + 3) = 2x(x + 43) Reorder the terms: 10(3 + x) = 2x(x + 43) (3 * 10 + x * 10) = 2x(x + 43) (30 + 10x) = 2x(x + 43) Reorder the terms: 30 + 10x = 2x(43 + x) 30 + 10x = (43 * 2x + x * 2x) 30 + 10x = (86x + 2x2) Solving 30 + 10x = 86x + 2x2 Solving for variable 'x'. Combine like terms: 10x + -86x = -76x 30 + -76x + -2x2 = 86x + 2x2 + -86x + -2x2 Reorder the terms: 30 + -76x + -2x2 = 86x + -86x + 2x2 + -2x2 Combine like terms: 86x + -86x = 0 30 + -76x + -2x2 = 0 + 2x2 + -2x2 30 + -76x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 30 + -76x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -38x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -38x + -1x2)' equal to zero and attempt to solve: Simplifying 15 + -38x + -1x2 = 0 Solving 15 + -38x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + 38x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 38x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 38x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 38x + x2 = 0 + 15 38x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 38x + x2 = 15 The x term is 38x. Take half its coefficient (19). Square it (361) and add it to both sides. Add '361' to each side of the equation. 38x + 361 + x2 = 15 + 361 Reorder the terms: 361 + 38x + x2 = 15 + 361 Combine like terms: 15 + 361 = 376 361 + 38x + x2 = 376 Factor a perfect square on the left side: (x + 19)(x + 19) = 376 Calculate the square root of the right side: 19.39071943 Break this problem into two subproblems by setting (x + 19) equal to 19.39071943 and -19.39071943.Subproblem 1
x + 19 = 19.39071943 Simplifying x + 19 = 19.39071943 Reorder the terms: 19 + x = 19.39071943 Solving 19 + x = 19.39071943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = 19.39071943 + -19 Combine like terms: 19 + -19 = 0 0 + x = 19.39071943 + -19 x = 19.39071943 + -19 Combine like terms: 19.39071943 + -19 = 0.39071943 x = 0.39071943 Simplifying x = 0.39071943Subproblem 2
x + 19 = -19.39071943 Simplifying x + 19 = -19.39071943 Reorder the terms: 19 + x = -19.39071943 Solving 19 + x = -19.39071943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = -19.39071943 + -19 Combine like terms: 19 + -19 = 0 0 + x = -19.39071943 + -19 x = -19.39071943 + -19 Combine like terms: -19.39071943 + -19 = -38.39071943 x = -38.39071943 Simplifying x = -38.39071943Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.39071943, -38.39071943}Solution
x = {0.39071943, -38.39071943}
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