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Simplifying 0.95 = 3x2 + -2.6x Reorder the terms: 0.95 = -2.6x + 3x2 Solving 0.95 = -2.6x + 3x2 Solving for variable 'x'. Reorder the terms: 0.95 + 2.6x + -3x2 = -2.6x + 2.6x + 3x2 + -3x2 Combine like terms: -2.6x + 2.6x = 0.0 0.95 + 2.6x + -3x2 = 0.0 + 3x2 + -3x2 0.95 + 2.6x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 0.95 + 2.6x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.3166666667 + -0.8666666667x + x2 = 0 Move the constant term to the right: Add '0.3166666667' to each side of the equation. -0.3166666667 + -0.8666666667x + 0.3166666667 + x2 = 0 + 0.3166666667 Reorder the terms: -0.3166666667 + 0.3166666667 + -0.8666666667x + x2 = 0 + 0.3166666667 Combine like terms: -0.3166666667 + 0.3166666667 = 0.0000000000 0.0000000000 + -0.8666666667x + x2 = 0 + 0.3166666667 -0.8666666667x + x2 = 0 + 0.3166666667 Combine like terms: 0 + 0.3166666667 = 0.3166666667 -0.8666666667x + x2 = 0.3166666667 The x term is -0.8666666667x. Take half its coefficient (-0.4333333334). Square it (0.1877777778) and add it to both sides. Add '0.1877777778' to each side of the equation. -0.8666666667x + 0.1877777778 + x2 = 0.3166666667 + 0.1877777778 Reorder the terms: 0.1877777778 + -0.8666666667x + x2 = 0.3166666667 + 0.1877777778 Combine like terms: 0.3166666667 + 0.1877777778 = 0.5044444445 0.1877777778 + -0.8666666667x + x2 = 0.5044444445 Factor a perfect square on the left side: (x + -0.4333333334)(x + -0.4333333334) = 0.5044444445 Calculate the square root of the right side: 0.710242525 Break this problem into two subproblems by setting (x + -0.4333333334) equal to 0.710242525 and -0.710242525.Subproblem 1
x + -0.4333333334 = 0.710242525 Simplifying x + -0.4333333334 = 0.710242525 Reorder the terms: -0.4333333334 + x = 0.710242525 Solving -0.4333333334 + x = 0.710242525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4333333334' to each side of the equation. -0.4333333334 + 0.4333333334 + x = 0.710242525 + 0.4333333334 Combine like terms: -0.4333333334 + 0.4333333334 = 0.0000000000 0.0000000000 + x = 0.710242525 + 0.4333333334 x = 0.710242525 + 0.4333333334 Combine like terms: 0.710242525 + 0.4333333334 = 1.1435758584 x = 1.1435758584 Simplifying x = 1.1435758584Subproblem 2
x + -0.4333333334 = -0.710242525 Simplifying x + -0.4333333334 = -0.710242525 Reorder the terms: -0.4333333334 + x = -0.710242525 Solving -0.4333333334 + x = -0.710242525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4333333334' to each side of the equation. -0.4333333334 + 0.4333333334 + x = -0.710242525 + 0.4333333334 Combine like terms: -0.4333333334 + 0.4333333334 = 0.0000000000 0.0000000000 + x = -0.710242525 + 0.4333333334 x = -0.710242525 + 0.4333333334 Combine like terms: -0.710242525 + 0.4333333334 = -0.2769091916 x = -0.2769091916 Simplifying x = -0.2769091916Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1435758584, -0.2769091916}
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