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Simplifying 4x2 + -6x + -1 = 10 Reorder the terms: -1 + -6x + 4x2 = 10 Solving -1 + -6x + 4x2 = 10 Solving for variable 'x'. Reorder the terms: -1 + -10 + -6x + 4x2 = 10 + -10 Combine like terms: -1 + -10 = -11 -11 + -6x + 4x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -11 + -6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + -1.5x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -1.5x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -1.5x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -1.5x + x2 = 0 + 2.75 -1.5x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -1.5x + x2 = 2.75 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 2.75 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 2.75 + 0.5625 Combine like terms: 2.75 + 0.5625 = 3.3125 0.5625 + -1.5x + x2 = 3.3125 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 3.3125 Calculate the square root of the right side: 1.820027472 Break this problem into two subproblems by setting (x + -0.75) equal to 1.820027472 and -1.820027472.Subproblem 1
x + -0.75 = 1.820027472 Simplifying x + -0.75 = 1.820027472 Reorder the terms: -0.75 + x = 1.820027472 Solving -0.75 + x = 1.820027472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.820027472 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.820027472 + 0.75 x = 1.820027472 + 0.75 Combine like terms: 1.820027472 + 0.75 = 2.570027472 x = 2.570027472 Simplifying x = 2.570027472Subproblem 2
x + -0.75 = -1.820027472 Simplifying x + -0.75 = -1.820027472 Reorder the terms: -0.75 + x = -1.820027472 Solving -0.75 + x = -1.820027472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.820027472 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.820027472 + 0.75 x = -1.820027472 + 0.75 Combine like terms: -1.820027472 + 0.75 = -1.070027472 x = -1.070027472 Simplifying x = -1.070027472Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.570027472, -1.070027472}
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