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Simplifying 19x + -15 = 2x2 Reorder the terms: -15 + 19x = 2x2 Solving -15 + 19x = 2x2 Solving for variable 'x'. Combine like terms: 2x2 + -2x2 = 0 -15 + 19x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 7.5 + -9.5x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -9.5x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -9.5x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -9.5x + x2 = 0 + -7.5 -9.5x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -9.5x + x2 = -7.5 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = -7.5 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = -7.5 + 22.5625 Combine like terms: -7.5 + 22.5625 = 15.0625 22.5625 + -9.5x + x2 = 15.0625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (x + -4.75) equal to 3.881043674 and -3.881043674.Subproblem 1
x + -4.75 = 3.881043674 Simplifying x + -4.75 = 3.881043674 Reorder the terms: -4.75 + x = 3.881043674 Solving -4.75 + x = 3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 3.881043674 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 3.881043674 + 4.75 x = 3.881043674 + 4.75 Combine like terms: 3.881043674 + 4.75 = 8.631043674 x = 8.631043674 Simplifying x = 8.631043674Subproblem 2
x + -4.75 = -3.881043674 Simplifying x + -4.75 = -3.881043674 Reorder the terms: -4.75 + x = -3.881043674 Solving -4.75 + x = -3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -3.881043674 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -3.881043674 + 4.75 x = -3.881043674 + 4.75 Combine like terms: -3.881043674 + 4.75 = 0.868956326 x = 0.868956326 Simplifying x = 0.868956326Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.631043674, 0.868956326}
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