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Simplifying 10x2 + -39x + 23 = 30 Reorder the terms: 23 + -39x + 10x2 = 30 Solving 23 + -39x + 10x2 = 30 Solving for variable 'x'. Reorder the terms: 23 + -30 + -39x + 10x2 = 30 + -30 Combine like terms: 23 + -30 = -7 -7 + -39x + 10x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -7 + -39x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.7 + -3.9x + x2 = 0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + -3.9x + 0.7 + x2 = 0 + 0.7 Reorder the terms: -0.7 + 0.7 + -3.9x + x2 = 0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + -3.9x + x2 = 0 + 0.7 -3.9x + x2 = 0 + 0.7 Combine like terms: 0 + 0.7 = 0.7 -3.9x + x2 = 0.7 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 = 0.7 + 3.8025 Reorder the terms: 3.8025 + -3.9x + x2 = 0.7 + 3.8025 Combine like terms: 0.7 + 3.8025 = 4.5025 3.8025 + -3.9x + x2 = 4.5025 Factor a perfect square on the left side: (x + -1.95)(x + -1.95) = 4.5025 Calculate the square root of the right side: 2.121909517 Break this problem into two subproblems by setting (x + -1.95) equal to 2.121909517 and -2.121909517.Subproblem 1
x + -1.95 = 2.121909517 Simplifying x + -1.95 = 2.121909517 Reorder the terms: -1.95 + x = 2.121909517 Solving -1.95 + x = 2.121909517 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 = 2.121909517 + 1.95 Combine like terms: -1.95 + 1.95 = 0.00 0.00 + x = 2.121909517 + 1.95 x = 2.121909517 + 1.95 Combine like terms: 2.121909517 + 1.95 = 4.071909517 x = 4.071909517 Simplifying x = 4.071909517Subproblem 2
x + -1.95 = -2.121909517 Simplifying x + -1.95 = -2.121909517 Reorder the terms: -1.95 + x = -2.121909517 Solving -1.95 + x = -2.121909517 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 = -2.121909517 + 1.95 Combine like terms: -1.95 + 1.95 = 0.00 0.00 + x = -2.121909517 + 1.95 x = -2.121909517 + 1.95 Combine like terms: -2.121909517 + 1.95 = -0.171909517 x = -0.171909517 Simplifying x = -0.171909517Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.071909517, -0.171909517}
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