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Simplifying 62x2 + 15x + -35 = 0 Reorder the terms: -35 + 15x + 62x2 = 0 Solving -35 + 15x + 62x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 62 the coefficient of the squared term: Divide each side by '62'. -0.564516129 + 0.2419354839x + x2 = 0 Move the constant term to the right: Add '0.564516129' to each side of the equation. -0.564516129 + 0.2419354839x + 0.564516129 + x2 = 0 + 0.564516129 Reorder the terms: -0.564516129 + 0.564516129 + 0.2419354839x + x2 = 0 + 0.564516129 Combine like terms: -0.564516129 + 0.564516129 = 0.000000000 0.000000000 + 0.2419354839x + x2 = 0 + 0.564516129 0.2419354839x + x2 = 0 + 0.564516129 Combine like terms: 0 + 0.564516129 = 0.564516129 0.2419354839x + x2 = 0.564516129 The x term is 0.2419354839x. Take half its coefficient (0.120967742). Square it (0.01463319460) and add it to both sides. Add '0.01463319460' to each side of the equation. 0.2419354839x + 0.01463319460 + x2 = 0.564516129 + 0.01463319460 Reorder the terms: 0.01463319460 + 0.2419354839x + x2 = 0.564516129 + 0.01463319460 Combine like terms: 0.564516129 + 0.01463319460 = 0.5791493236 0.01463319460 + 0.2419354839x + x2 = 0.5791493236 Factor a perfect square on the left side: (x + 0.120967742)(x + 0.120967742) = 0.5791493236 Calculate the square root of the right side: 0.761018609 Break this problem into two subproblems by setting (x + 0.120967742) equal to 0.761018609 and -0.761018609.Subproblem 1
x + 0.120967742 = 0.761018609 Simplifying x + 0.120967742 = 0.761018609 Reorder the terms: 0.120967742 + x = 0.761018609 Solving 0.120967742 + x = 0.761018609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.120967742' to each side of the equation. 0.120967742 + -0.120967742 + x = 0.761018609 + -0.120967742 Combine like terms: 0.120967742 + -0.120967742 = 0.000000000 0.000000000 + x = 0.761018609 + -0.120967742 x = 0.761018609 + -0.120967742 Combine like terms: 0.761018609 + -0.120967742 = 0.640050867 x = 0.640050867 Simplifying x = 0.640050867Subproblem 2
x + 0.120967742 = -0.761018609 Simplifying x + 0.120967742 = -0.761018609 Reorder the terms: 0.120967742 + x = -0.761018609 Solving 0.120967742 + x = -0.761018609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.120967742' to each side of the equation. 0.120967742 + -0.120967742 + x = -0.761018609 + -0.120967742 Combine like terms: 0.120967742 + -0.120967742 = 0.000000000 0.000000000 + x = -0.761018609 + -0.120967742 x = -0.761018609 + -0.120967742 Combine like terms: -0.761018609 + -0.120967742 = -0.881986351 x = -0.881986351 Simplifying x = -0.881986351Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.640050867, -0.881986351}
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