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Simplifying -5.64x2 + 3.64x + 1.62 = 0 Reorder the terms: 1.62 + 3.64x + -5.64x2 = 0 Solving 1.62 + 3.64x + -5.64x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5.64 the coefficient of the squared term: Divide each side by '-5.64'. -0.2872340426 + -0.6453900709x + x2 = 0 Move the constant term to the right: Add '0.2872340426' to each side of the equation. -0.2872340426 + -0.6453900709x + 0.2872340426 + x2 = 0 + 0.2872340426 Reorder the terms: -0.2872340426 + 0.2872340426 + -0.6453900709x + x2 = 0 + 0.2872340426 Combine like terms: -0.2872340426 + 0.2872340426 = 0.0000000000 0.0000000000 + -0.6453900709x + x2 = 0 + 0.2872340426 -0.6453900709x + x2 = 0 + 0.2872340426 Combine like terms: 0 + 0.2872340426 = 0.2872340426 -0.6453900709x + x2 = 0.2872340426 The x term is -0.6453900709x. Take half its coefficient (-0.3226950355). Square it (0.1041320859) and add it to both sides. Add '0.1041320859' to each side of the equation. -0.6453900709x + 0.1041320859 + x2 = 0.2872340426 + 0.1041320859 Reorder the terms: 0.1041320859 + -0.6453900709x + x2 = 0.2872340426 + 0.1041320859 Combine like terms: 0.2872340426 + 0.1041320859 = 0.3913661285 0.1041320859 + -0.6453900709x + x2 = 0.3913661285 Factor a perfect square on the left side: (x + -0.3226950355)(x + -0.3226950355) = 0.3913661285 Calculate the square root of the right side: 0.625592622 Break this problem into two subproblems by setting (x + -0.3226950355) equal to 0.625592622 and -0.625592622.Subproblem 1
x + -0.3226950355 = 0.625592622 Simplifying x + -0.3226950355 = 0.625592622 Reorder the terms: -0.3226950355 + x = 0.625592622 Solving -0.3226950355 + x = 0.625592622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3226950355' to each side of the equation. -0.3226950355 + 0.3226950355 + x = 0.625592622 + 0.3226950355 Combine like terms: -0.3226950355 + 0.3226950355 = 0.0000000000 0.0000000000 + x = 0.625592622 + 0.3226950355 x = 0.625592622 + 0.3226950355 Combine like terms: 0.625592622 + 0.3226950355 = 0.9482876575 x = 0.9482876575 Simplifying x = 0.9482876575Subproblem 2
x + -0.3226950355 = -0.625592622 Simplifying x + -0.3226950355 = -0.625592622 Reorder the terms: -0.3226950355 + x = -0.625592622 Solving -0.3226950355 + x = -0.625592622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3226950355' to each side of the equation. -0.3226950355 + 0.3226950355 + x = -0.625592622 + 0.3226950355 Combine like terms: -0.3226950355 + 0.3226950355 = 0.0000000000 0.0000000000 + x = -0.625592622 + 0.3226950355 x = -0.625592622 + 0.3226950355 Combine like terms: -0.625592622 + 0.3226950355 = -0.3028975865 x = -0.3028975865 Simplifying x = -0.3028975865Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9482876575, -0.3028975865}
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