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Simplifying 2x2 + 19x = 35 Reorder the terms: 19x + 2x2 = 35 Solving 19x + 2x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + 19x + 2x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + 9.5x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + 9.5x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + 9.5x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + 9.5x + x2 = 0 + 17.5 9.5x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 9.5x + x2 = 17.5 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 = 17.5 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 17.5 + 22.5625 Combine like terms: 17.5 + 22.5625 = 40.0625 22.5625 + 9.5x + x2 = 40.0625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 40.0625 Calculate the square root of the right side: 6.329494451 Break this problem into two subproblems by setting (x + 4.75) equal to 6.329494451 and -6.329494451.Subproblem 1
x + 4.75 = 6.329494451 Simplifying x + 4.75 = 6.329494451 Reorder the terms: 4.75 + x = 6.329494451 Solving 4.75 + x = 6.329494451 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 = 6.329494451 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 6.329494451 + -4.75 x = 6.329494451 + -4.75 Combine like terms: 6.329494451 + -4.75 = 1.579494451 x = 1.579494451 Simplifying x = 1.579494451Subproblem 2
x + 4.75 = -6.329494451 Simplifying x + 4.75 = -6.329494451 Reorder the terms: 4.75 + x = -6.329494451 Solving 4.75 + x = -6.329494451 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 = -6.329494451 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -6.329494451 + -4.75 x = -6.329494451 + -4.75 Combine like terms: -6.329494451 + -4.75 = -11.079494451 x = -11.079494451 Simplifying x = -11.079494451Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.579494451, -11.079494451}
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