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Simplifying 0.67 + 1.19x + -1x2 = 0 Solving 0.67 + 1.19x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.67 + -1.19x + x2 = 0 Move the constant term to the right: Add '0.67' to each side of the equation. -0.67 + -1.19x + 0.67 + x2 = 0 + 0.67 Reorder the terms: -0.67 + 0.67 + -1.19x + x2 = 0 + 0.67 Combine like terms: -0.67 + 0.67 = 0.00 0.00 + -1.19x + x2 = 0 + 0.67 -1.19x + x2 = 0 + 0.67 Combine like terms: 0 + 0.67 = 0.67 -1.19x + x2 = 0.67 The x term is -1.19x. Take half its coefficient (-0.595). Square it (0.354025) and add it to both sides. Add '0.354025' to each side of the equation. -1.19x + 0.354025 + x2 = 0.67 + 0.354025 Reorder the terms: 0.354025 + -1.19x + x2 = 0.67 + 0.354025 Combine like terms: 0.67 + 0.354025 = 1.024025 0.354025 + -1.19x + x2 = 1.024025 Factor a perfect square on the left side: (x + -0.595)(x + -0.595) = 1.024025 Calculate the square root of the right side: 1.011941204 Break this problem into two subproblems by setting (x + -0.595) equal to 1.011941204 and -1.011941204.Subproblem 1
x + -0.595 = 1.011941204 Simplifying x + -0.595 = 1.011941204 Reorder the terms: -0.595 + x = 1.011941204 Solving -0.595 + x = 1.011941204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.595' to each side of the equation. -0.595 + 0.595 + x = 1.011941204 + 0.595 Combine like terms: -0.595 + 0.595 = 0.000 0.000 + x = 1.011941204 + 0.595 x = 1.011941204 + 0.595 Combine like terms: 1.011941204 + 0.595 = 1.606941204 x = 1.606941204 Simplifying x = 1.606941204Subproblem 2
x + -0.595 = -1.011941204 Simplifying x + -0.595 = -1.011941204 Reorder the terms: -0.595 + x = -1.011941204 Solving -0.595 + x = -1.011941204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.595' to each side of the equation. -0.595 + 0.595 + x = -1.011941204 + 0.595 Combine like terms: -0.595 + 0.595 = 0.000 0.000 + x = -1.011941204 + 0.595 x = -1.011941204 + 0.595 Combine like terms: -1.011941204 + 0.595 = -0.416941204 x = -0.416941204 Simplifying x = -0.416941204Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.606941204, -0.416941204}
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