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Simplifying 510x2 + -33x + -10 = 0 Reorder the terms: -10 + -33x + 510x2 = 0 Solving -10 + -33x + 510x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 510 the coefficient of the squared term: Divide each side by '510'. -0.01960784314 + -0.06470588235x + x2 = 0 Move the constant term to the right: Add '0.01960784314' to each side of the equation. -0.01960784314 + -0.06470588235x + 0.01960784314 + x2 = 0 + 0.01960784314 Reorder the terms: -0.01960784314 + 0.01960784314 + -0.06470588235x + x2 = 0 + 0.01960784314 Combine like terms: -0.01960784314 + 0.01960784314 = 0.00000000000 0.00000000000 + -0.06470588235x + x2 = 0 + 0.01960784314 -0.06470588235x + x2 = 0 + 0.01960784314 Combine like terms: 0 + 0.01960784314 = 0.01960784314 -0.06470588235x + x2 = 0.01960784314 The x term is -0.06470588235x. Take half its coefficient (-0.03235294118). Square it (0.001046712803) and add it to both sides. Add '0.001046712803' to each side of the equation. -0.06470588235x + 0.001046712803 + x2 = 0.01960784314 + 0.001046712803 Reorder the terms: 0.001046712803 + -0.06470588235x + x2 = 0.01960784314 + 0.001046712803 Combine like terms: 0.01960784314 + 0.001046712803 = 0.020654555943 0.001046712803 + -0.06470588235x + x2 = 0.020654555943 Factor a perfect square on the left side: (x + -0.03235294118)(x + -0.03235294118) = 0.020654555943 Calculate the square root of the right side: 0.14371693 Break this problem into two subproblems by setting (x + -0.03235294118) equal to 0.14371693 and -0.14371693.Subproblem 1
x + -0.03235294118 = 0.14371693 Simplifying x + -0.03235294118 = 0.14371693 Reorder the terms: -0.03235294118 + x = 0.14371693 Solving -0.03235294118 + x = 0.14371693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03235294118' to each side of the equation. -0.03235294118 + 0.03235294118 + x = 0.14371693 + 0.03235294118 Combine like terms: -0.03235294118 + 0.03235294118 = 0.00000000000 0.00000000000 + x = 0.14371693 + 0.03235294118 x = 0.14371693 + 0.03235294118 Combine like terms: 0.14371693 + 0.03235294118 = 0.17606987118 x = 0.17606987118 Simplifying x = 0.17606987118Subproblem 2
x + -0.03235294118 = -0.14371693 Simplifying x + -0.03235294118 = -0.14371693 Reorder the terms: -0.03235294118 + x = -0.14371693 Solving -0.03235294118 + x = -0.14371693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03235294118' to each side of the equation. -0.03235294118 + 0.03235294118 + x = -0.14371693 + 0.03235294118 Combine like terms: -0.03235294118 + 0.03235294118 = 0.00000000000 0.00000000000 + x = -0.14371693 + 0.03235294118 x = -0.14371693 + 0.03235294118 Combine like terms: -0.14371693 + 0.03235294118 = -0.11136398882 x = -0.11136398882 Simplifying x = -0.11136398882Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.17606987118, -0.11136398882}
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