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Simplifying 14x2 + -19x = x + 9x2 + 37 Reorder the terms: -19x + 14x2 = x + 9x2 + 37 Reorder the terms: -19x + 14x2 = 37 + x + 9x2 Solving -19x + 14x2 = 37 + x + 9x2 Solving for variable 'x'. Reorder the terms: -37 + -19x + -1x + 14x2 + -9x2 = 37 + x + 9x2 + -37 + -1x + -9x2 Combine like terms: -19x + -1x = -20x -37 + -20x + 14x2 + -9x2 = 37 + x + 9x2 + -37 + -1x + -9x2 Combine like terms: 14x2 + -9x2 = 5x2 -37 + -20x + 5x2 = 37 + x + 9x2 + -37 + -1x + -9x2 Reorder the terms: -37 + -20x + 5x2 = 37 + -37 + x + -1x + 9x2 + -9x2 Combine like terms: 37 + -37 = 0 -37 + -20x + 5x2 = 0 + x + -1x + 9x2 + -9x2 -37 + -20x + 5x2 = x + -1x + 9x2 + -9x2 Combine like terms: x + -1x = 0 -37 + -20x + 5x2 = 0 + 9x2 + -9x2 -37 + -20x + 5x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -37 + -20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.4 + -4x + x2 = 0 Move the constant term to the right: Add '7.4' to each side of the equation. -7.4 + -4x + 7.4 + x2 = 0 + 7.4 Reorder the terms: -7.4 + 7.4 + -4x + x2 = 0 + 7.4 Combine like terms: -7.4 + 7.4 = 0.0 0.0 + -4x + x2 = 0 + 7.4 -4x + x2 = 0 + 7.4 Combine like terms: 0 + 7.4 = 7.4 -4x + x2 = 7.4 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 7.4 + 4 Reorder the terms: 4 + -4x + x2 = 7.4 + 4 Combine like terms: 7.4 + 4 = 11.4 4 + -4x + x2 = 11.4 Factor a perfect square on the left side: (x + -2)(x + -2) = 11.4 Calculate the square root of the right side: 3.376388603 Break this problem into two subproblems by setting (x + -2) equal to 3.376388603 and -3.376388603.Subproblem 1
x + -2 = 3.376388603 Simplifying x + -2 = 3.376388603 Reorder the terms: -2 + x = 3.376388603 Solving -2 + x = 3.376388603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.376388603 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.376388603 + 2 x = 3.376388603 + 2 Combine like terms: 3.376388603 + 2 = 5.376388603 x = 5.376388603 Simplifying x = 5.376388603Subproblem 2
x + -2 = -3.376388603 Simplifying x + -2 = -3.376388603 Reorder the terms: -2 + x = -3.376388603 Solving -2 + x = -3.376388603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.376388603 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.376388603 + 2 x = -3.376388603 + 2 Combine like terms: -3.376388603 + 2 = -1.376388603 x = -1.376388603 Simplifying x = -1.376388603Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.376388603, -1.376388603}
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