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Simplifying 0.33x2 + -1(-2.5x) + 1 = 0 Remove parenthesis around (-2.5x) 0.33x2 + -1 * -2.5x + 1 = 0 Multiply -1 * -2.5 0.33x2 + 2.5x + 1 = 0 Reorder the terms: 1 + 2.5x + 0.33x2 = 0 Solving 1 + 2.5x + 0.33x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.33 the coefficient of the squared term: Divide each side by '0.33'. 3.03030303 + 7.575757576x + x2 = 0 Move the constant term to the right: Add '-3.03030303' to each side of the equation. 3.03030303 + 7.575757576x + -3.03030303 + x2 = 0 + -3.03030303 Reorder the terms: 3.03030303 + -3.03030303 + 7.575757576x + x2 = 0 + -3.03030303 Combine like terms: 3.03030303 + -3.03030303 = 0.00000000 0.00000000 + 7.575757576x + x2 = 0 + -3.03030303 7.575757576x + x2 = 0 + -3.03030303 Combine like terms: 0 + -3.03030303 = -3.03030303 7.575757576x + x2 = -3.03030303 The x term is 7.575757576x. Take half its coefficient (3.787878788). Square it (14.34802571) and add it to both sides. Add '14.34802571' to each side of the equation. 7.575757576x + 14.34802571 + x2 = -3.03030303 + 14.34802571 Reorder the terms: 14.34802571 + 7.575757576x + x2 = -3.03030303 + 14.34802571 Combine like terms: -3.03030303 + 14.34802571 = 11.31772268 14.34802571 + 7.575757576x + x2 = 11.31772268 Factor a perfect square on the left side: (x + 3.787878788)(x + 3.787878788) = 11.31772268 Calculate the square root of the right side: 3.36418232 Break this problem into two subproblems by setting (x + 3.787878788) equal to 3.36418232 and -3.36418232.Subproblem 1
x + 3.787878788 = 3.36418232 Simplifying x + 3.787878788 = 3.36418232 Reorder the terms: 3.787878788 + x = 3.36418232 Solving 3.787878788 + x = 3.36418232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.787878788' to each side of the equation. 3.787878788 + -3.787878788 + x = 3.36418232 + -3.787878788 Combine like terms: 3.787878788 + -3.787878788 = 0.000000000 0.000000000 + x = 3.36418232 + -3.787878788 x = 3.36418232 + -3.787878788 Combine like terms: 3.36418232 + -3.787878788 = -0.423696468 x = -0.423696468 Simplifying x = -0.423696468Subproblem 2
x + 3.787878788 = -3.36418232 Simplifying x + 3.787878788 = -3.36418232 Reorder the terms: 3.787878788 + x = -3.36418232 Solving 3.787878788 + x = -3.36418232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.787878788' to each side of the equation. 3.787878788 + -3.787878788 + x = -3.36418232 + -3.787878788 Combine like terms: 3.787878788 + -3.787878788 = 0.000000000 0.000000000 + x = -3.36418232 + -3.787878788 x = -3.36418232 + -3.787878788 Combine like terms: -3.36418232 + -3.787878788 = -7.152061108 x = -7.152061108 Simplifying x = -7.152061108Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.423696468, -7.152061108}
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