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Simplifying 10x2 + -19x + 5 = 0 Reorder the terms: 5 + -19x + 10x2 = 0 Solving 5 + -19x + 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'. 0.5 + -1.9x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.9x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.9x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.9x + x2 = 0 + -0.5 -1.9x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1.9x + x2 = -0.5 The x term is -1.9x. Take half its coefficient (-0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. -1.9x + 0.9025 + x2 = -0.5 + 0.9025 Reorder the terms: 0.9025 + -1.9x + x2 = -0.5 + 0.9025 Combine like terms: -0.5 + 0.9025 = 0.4025 0.9025 + -1.9x + x2 = 0.4025 Factor a perfect square on the left side: (x + -0.95)(x + -0.95) = 0.4025 Calculate the square root of the right side: 0.634428877 Break this problem into two subproblems by setting (x + -0.95) equal to 0.634428877 and -0.634428877.Subproblem 1
x + -0.95 = 0.634428877 Simplifying x + -0.95 = 0.634428877 Reorder the terms: -0.95 + x = 0.634428877 Solving -0.95 + x = 0.634428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + x = 0.634428877 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + x = 0.634428877 + 0.95 x = 0.634428877 + 0.95 Combine like terms: 0.634428877 + 0.95 = 1.584428877 x = 1.584428877 Simplifying x = 1.584428877Subproblem 2
x + -0.95 = -0.634428877 Simplifying x + -0.95 = -0.634428877 Reorder the terms: -0.95 + x = -0.634428877 Solving -0.95 + x = -0.634428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + x = -0.634428877 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + x = -0.634428877 + 0.95 x = -0.634428877 + 0.95 Combine like terms: -0.634428877 + 0.95 = 0.315571123 x = 0.315571123 Simplifying x = 0.315571123Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.584428877, 0.315571123}
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