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Simplifying -4.905x2 + 1.69x + -0.03 = 0 Reorder the terms: -0.03 + 1.69x + -4.905x2 = 0 Solving -0.03 + 1.69x + -4.905x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.905 the coefficient of the squared term: Divide each side by '-4.905'. 0.006116207951 + -0.3445463812x + x2 = 0 Move the constant term to the right: Add '-0.006116207951' to each side of the equation. 0.006116207951 + -0.3445463812x + -0.006116207951 + x2 = 0 + -0.006116207951 Reorder the terms: 0.006116207951 + -0.006116207951 + -0.3445463812x + x2 = 0 + -0.006116207951 Combine like terms: 0.006116207951 + -0.006116207951 = 0.000000000000 0.000000000000 + -0.3445463812x + x2 = 0 + -0.006116207951 -0.3445463812x + x2 = 0 + -0.006116207951 Combine like terms: 0 + -0.006116207951 = -0.006116207951 -0.3445463812x + x2 = -0.006116207951 The x term is -0.3445463812x. Take half its coefficient (-0.1722731906). Square it (0.02967805220) and add it to both sides. Add '0.02967805220' to each side of the equation. -0.3445463812x + 0.02967805220 + x2 = -0.006116207951 + 0.02967805220 Reorder the terms: 0.02967805220 + -0.3445463812x + x2 = -0.006116207951 + 0.02967805220 Combine like terms: -0.006116207951 + 0.02967805220 = 0.023561844249 0.02967805220 + -0.3445463812x + x2 = 0.023561844249 Factor a perfect square on the left side: (x + -0.1722731906)(x + -0.1722731906) = 0.023561844249 Calculate the square root of the right side: 0.153498678 Break this problem into two subproblems by setting (x + -0.1722731906) equal to 0.153498678 and -0.153498678.Subproblem 1
x + -0.1722731906 = 0.153498678 Simplifying x + -0.1722731906 = 0.153498678 Reorder the terms: -0.1722731906 + x = 0.153498678 Solving -0.1722731906 + x = 0.153498678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1722731906' to each side of the equation. -0.1722731906 + 0.1722731906 + x = 0.153498678 + 0.1722731906 Combine like terms: -0.1722731906 + 0.1722731906 = 0.0000000000 0.0000000000 + x = 0.153498678 + 0.1722731906 x = 0.153498678 + 0.1722731906 Combine like terms: 0.153498678 + 0.1722731906 = 0.3257718686 x = 0.3257718686 Simplifying x = 0.3257718686Subproblem 2
x + -0.1722731906 = -0.153498678 Simplifying x + -0.1722731906 = -0.153498678 Reorder the terms: -0.1722731906 + x = -0.153498678 Solving -0.1722731906 + x = -0.153498678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1722731906' to each side of the equation. -0.1722731906 + 0.1722731906 + x = -0.153498678 + 0.1722731906 Combine like terms: -0.1722731906 + 0.1722731906 = 0.0000000000 0.0000000000 + x = -0.153498678 + 0.1722731906 x = -0.153498678 + 0.1722731906 Combine like terms: -0.153498678 + 0.1722731906 = 0.0187745126 x = 0.0187745126 Simplifying x = 0.0187745126Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3257718686, 0.0187745126}
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