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Simplifying 4x2 + 5.11x + -0.11 = 0 Reorder the terms: -0.11 + 5.11x + 4x2 = 0 Solving -0.11 + 5.11x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.0275 + 1.2775x + x2 = 0 Move the constant term to the right: Add '0.0275' to each side of the equation. -0.0275 + 1.2775x + 0.0275 + x2 = 0 + 0.0275 Reorder the terms: -0.0275 + 0.0275 + 1.2775x + x2 = 0 + 0.0275 Combine like terms: -0.0275 + 0.0275 = 0.0000 0.0000 + 1.2775x + x2 = 0 + 0.0275 1.2775x + x2 = 0 + 0.0275 Combine like terms: 0 + 0.0275 = 0.0275 1.2775x + x2 = 0.0275 The x term is 1.2775x. Take half its coefficient (0.63875). Square it (0.4080015625) and add it to both sides. Add '0.4080015625' to each side of the equation. 1.2775x + 0.4080015625 + x2 = 0.0275 + 0.4080015625 Reorder the terms: 0.4080015625 + 1.2775x + x2 = 0.0275 + 0.4080015625 Combine like terms: 0.0275 + 0.4080015625 = 0.4355015625 0.4080015625 + 1.2775x + x2 = 0.4355015625 Factor a perfect square on the left side: (x + 0.63875)(x + 0.63875) = 0.4355015625 Calculate the square root of the right side: 0.659925422 Break this problem into two subproblems by setting (x + 0.63875) equal to 0.659925422 and -0.659925422.Subproblem 1
x + 0.63875 = 0.659925422 Simplifying x + 0.63875 = 0.659925422 Reorder the terms: 0.63875 + x = 0.659925422 Solving 0.63875 + x = 0.659925422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.63875' to each side of the equation. 0.63875 + -0.63875 + x = 0.659925422 + -0.63875 Combine like terms: 0.63875 + -0.63875 = 0.00000 0.00000 + x = 0.659925422 + -0.63875 x = 0.659925422 + -0.63875 Combine like terms: 0.659925422 + -0.63875 = 0.021175422 x = 0.021175422 Simplifying x = 0.021175422Subproblem 2
x + 0.63875 = -0.659925422 Simplifying x + 0.63875 = -0.659925422 Reorder the terms: 0.63875 + x = -0.659925422 Solving 0.63875 + x = -0.659925422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.63875' to each side of the equation. 0.63875 + -0.63875 + x = -0.659925422 + -0.63875 Combine like terms: 0.63875 + -0.63875 = 0.00000 0.00000 + x = -0.659925422 + -0.63875 x = -0.659925422 + -0.63875 Combine like terms: -0.659925422 + -0.63875 = -1.298675422 x = -1.298675422 Simplifying x = -1.298675422Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.021175422, -1.298675422}
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