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Simplifying -10x2 + 39x + 24 = 0 Reorder the terms: 24 + 39x + -10x2 = 0 Solving 24 + 39x + -10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -2.4 + -3.9x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -3.9x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -3.9x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -3.9x + x2 = 0 + 2.4 -3.9x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -3.9x + x2 = 2.4 The x term is -3.9x. Take half its coefficient (-1.95). Square it (3.8025) and add it to both sides. Add '3.8025' to each side of the equation. -3.9x + 3.8025 + x2 = 2.4 + 3.8025 Reorder the terms: 3.8025 + -3.9x + x2 = 2.4 + 3.8025 Combine like terms: 2.4 + 3.8025 = 6.2025 3.8025 + -3.9x + x2 = 6.2025 Factor a perfect square on the left side: (x + -1.95)(x + -1.95) = 6.2025 Calculate the square root of the right side: 2.490481881 Break this problem into two subproblems by setting (x + -1.95) equal to 2.490481881 and -2.490481881.Subproblem 1
x + -1.95 = 2.490481881 Simplifying x + -1.95 = 2.490481881 Reorder the terms: -1.95 + x = 2.490481881 Solving -1.95 + x = 2.490481881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.95' to each side of the equation. -1.95 + 1.95 + x = 2.490481881 + 1.95 Combine like terms: -1.95 + 1.95 = 0.00 0.00 + x = 2.490481881 + 1.95 x = 2.490481881 + 1.95 Combine like terms: 2.490481881 + 1.95 = 4.440481881 x = 4.440481881 Simplifying x = 4.440481881Subproblem 2
x + -1.95 = -2.490481881 Simplifying x + -1.95 = -2.490481881 Reorder the terms: -1.95 + x = -2.490481881 Solving -1.95 + x = -2.490481881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.95' to each side of the equation. -1.95 + 1.95 + x = -2.490481881 + 1.95 Combine like terms: -1.95 + 1.95 = 0.00 0.00 + x = -2.490481881 + 1.95 x = -2.490481881 + 1.95 Combine like terms: -2.490481881 + 1.95 = -0.540481881 x = -0.540481881 Simplifying x = -0.540481881Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.440481881, -0.540481881}
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