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Simplifying 6.52x2 + 3.68x + -4.65 = 0 Reorder the terms: -4.65 + 3.68x + 6.52x2 = 0 Solving -4.65 + 3.68x + 6.52x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6.52 the coefficient of the squared term: Divide each side by '6.52'. -0.713190184 + 0.5644171779x + x2 = 0 Move the constant term to the right: Add '0.713190184' to each side of the equation. -0.713190184 + 0.5644171779x + 0.713190184 + x2 = 0 + 0.713190184 Reorder the terms: -0.713190184 + 0.713190184 + 0.5644171779x + x2 = 0 + 0.713190184 Combine like terms: -0.713190184 + 0.713190184 = 0.000000000 0.000000000 + 0.5644171779x + x2 = 0 + 0.713190184 0.5644171779x + x2 = 0 + 0.713190184 Combine like terms: 0 + 0.713190184 = 0.713190184 0.5644171779x + x2 = 0.713190184 The x term is 0.5644171779x. Take half its coefficient (0.282208589). Square it (0.07964168771) and add it to both sides. Add '0.07964168771' to each side of the equation. 0.5644171779x + 0.07964168771 + x2 = 0.713190184 + 0.07964168771 Reorder the terms: 0.07964168771 + 0.5644171779x + x2 = 0.713190184 + 0.07964168771 Combine like terms: 0.713190184 + 0.07964168771 = 0.79283187171 0.07964168771 + 0.5644171779x + x2 = 0.79283187171 Factor a perfect square on the left side: (x + 0.282208589)(x + 0.282208589) = 0.79283187171 Calculate the square root of the right side: 0.890411069 Break this problem into two subproblems by setting (x + 0.282208589) equal to 0.890411069 and -0.890411069.Subproblem 1
x + 0.282208589 = 0.890411069 Simplifying x + 0.282208589 = 0.890411069 Reorder the terms: 0.282208589 + x = 0.890411069 Solving 0.282208589 + x = 0.890411069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.282208589' to each side of the equation. 0.282208589 + -0.282208589 + x = 0.890411069 + -0.282208589 Combine like terms: 0.282208589 + -0.282208589 = 0.000000000 0.000000000 + x = 0.890411069 + -0.282208589 x = 0.890411069 + -0.282208589 Combine like terms: 0.890411069 + -0.282208589 = 0.60820248 x = 0.60820248 Simplifying x = 0.60820248Subproblem 2
x + 0.282208589 = -0.890411069 Simplifying x + 0.282208589 = -0.890411069 Reorder the terms: 0.282208589 + x = -0.890411069 Solving 0.282208589 + x = -0.890411069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.282208589' to each side of the equation. 0.282208589 + -0.282208589 + x = -0.890411069 + -0.282208589 Combine like terms: 0.282208589 + -0.282208589 = 0.000000000 0.000000000 + x = -0.890411069 + -0.282208589 x = -0.890411069 + -0.282208589 Combine like terms: -0.890411069 + -0.282208589 = -1.172619658 x = -1.172619658 Simplifying x = -1.172619658Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.60820248, -1.172619658}
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