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Simplifying 1.34x2 + -1.1x = 1.02 Reorder the terms: -1.1x + 1.34x2 = 1.02 Solving -1.1x + 1.34x2 = 1.02 Solving for variable 'x'. Reorder the terms: -1.02 + -1.1x + 1.34x2 = 1.02 + -1.02 Combine like terms: 1.02 + -1.02 = 0.00 -1.02 + -1.1x + 1.34x2 = 0.00 Begin completing the square. Divide all terms by 1.34 the coefficient of the squared term: Divide each side by '1.34'. -0.7611940299 + -0.8208955224x + x2 = 0 Move the constant term to the right: Add '0.7611940299' to each side of the equation. -0.7611940299 + -0.8208955224x + 0.7611940299 + x2 = 0 + 0.7611940299 Reorder the terms: -0.7611940299 + 0.7611940299 + -0.8208955224x + x2 = 0 + 0.7611940299 Combine like terms: -0.7611940299 + 0.7611940299 = 0.0000000000 0.0000000000 + -0.8208955224x + x2 = 0 + 0.7611940299 -0.8208955224x + x2 = 0 + 0.7611940299 Combine like terms: 0 + 0.7611940299 = 0.7611940299 -0.8208955224x + x2 = 0.7611940299 The x term is -0.8208955224x. Take half its coefficient (-0.4104477612). Square it (0.1684673647) and add it to both sides. Add '0.1684673647' to each side of the equation. -0.8208955224x + 0.1684673647 + x2 = 0.7611940299 + 0.1684673647 Reorder the terms: 0.1684673647 + -0.8208955224x + x2 = 0.7611940299 + 0.1684673647 Combine like terms: 0.7611940299 + 0.1684673647 = 0.9296613946 0.1684673647 + -0.8208955224x + x2 = 0.9296613946 Factor a perfect square on the left side: (x + -0.4104477612)(x + -0.4104477612) = 0.9296613946 Calculate the square root of the right side: 0.964189501 Break this problem into two subproblems by setting (x + -0.4104477612) equal to 0.964189501 and -0.964189501.Subproblem 1
x + -0.4104477612 = 0.964189501 Simplifying x + -0.4104477612 = 0.964189501 Reorder the terms: -0.4104477612 + x = 0.964189501 Solving -0.4104477612 + x = 0.964189501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4104477612' to each side of the equation. -0.4104477612 + 0.4104477612 + x = 0.964189501 + 0.4104477612 Combine like terms: -0.4104477612 + 0.4104477612 = 0.0000000000 0.0000000000 + x = 0.964189501 + 0.4104477612 x = 0.964189501 + 0.4104477612 Combine like terms: 0.964189501 + 0.4104477612 = 1.3746372622 x = 1.3746372622 Simplifying x = 1.3746372622Subproblem 2
x + -0.4104477612 = -0.964189501 Simplifying x + -0.4104477612 = -0.964189501 Reorder the terms: -0.4104477612 + x = -0.964189501 Solving -0.4104477612 + x = -0.964189501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4104477612' to each side of the equation. -0.4104477612 + 0.4104477612 + x = -0.964189501 + 0.4104477612 Combine like terms: -0.4104477612 + 0.4104477612 = 0.0000000000 0.0000000000 + x = -0.964189501 + 0.4104477612 x = -0.964189501 + 0.4104477612 Combine like terms: -0.964189501 + 0.4104477612 = -0.5537417398 x = -0.5537417398 Simplifying x = -0.5537417398Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3746372622, -0.5537417398}
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