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Simplifying 24x2 + 38x + -15 = 0 Reorder the terms: -15 + 38x + 24x2 = 0 Solving -15 + 38x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.625 + 1.583333333x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 1.583333333x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 1.583333333x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 1.583333333x + x2 = 0 + 0.625 1.583333333x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 1.583333333x + x2 = 0.625 The x term is 1.583333333x. Take half its coefficient (0.7916666665). Square it (0.6267361108) and add it to both sides. Add '0.6267361108' to each side of the equation. 1.583333333x + 0.6267361108 + x2 = 0.625 + 0.6267361108 Reorder the terms: 0.6267361108 + 1.583333333x + x2 = 0.625 + 0.6267361108 Combine like terms: 0.625 + 0.6267361108 = 1.2517361108 0.6267361108 + 1.583333333x + x2 = 1.2517361108 Factor a perfect square on the left side: (x + 0.7916666665)(x + 0.7916666665) = 1.2517361108 Calculate the square root of the right side: 1.118810132 Break this problem into two subproblems by setting (x + 0.7916666665) equal to 1.118810132 and -1.118810132.Subproblem 1
x + 0.7916666665 = 1.118810132 Simplifying x + 0.7916666665 = 1.118810132 Reorder the terms: 0.7916666665 + x = 1.118810132 Solving 0.7916666665 + x = 1.118810132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7916666665' to each side of the equation. 0.7916666665 + -0.7916666665 + x = 1.118810132 + -0.7916666665 Combine like terms: 0.7916666665 + -0.7916666665 = 0.0000000000 0.0000000000 + x = 1.118810132 + -0.7916666665 x = 1.118810132 + -0.7916666665 Combine like terms: 1.118810132 + -0.7916666665 = 0.3271434655 x = 0.3271434655 Simplifying x = 0.3271434655Subproblem 2
x + 0.7916666665 = -1.118810132 Simplifying x + 0.7916666665 = -1.118810132 Reorder the terms: 0.7916666665 + x = -1.118810132 Solving 0.7916666665 + x = -1.118810132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7916666665' to each side of the equation. 0.7916666665 + -0.7916666665 + x = -1.118810132 + -0.7916666665 Combine like terms: 0.7916666665 + -0.7916666665 = 0.0000000000 0.0000000000 + x = -1.118810132 + -0.7916666665 x = -1.118810132 + -0.7916666665 Combine like terms: -1.118810132 + -0.7916666665 = -1.9104767985 x = -1.9104767985 Simplifying x = -1.9104767985Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3271434655, -1.9104767985}
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