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Simplifying 2x2 + -38x = 7x2 + -3x + -24 Reorder the terms: -38x + 2x2 = 7x2 + -3x + -24 Reorder the terms: -38x + 2x2 = -24 + -3x + 7x2 Solving -38x + 2x2 = -24 + -3x + 7x2 Solving for variable 'x'. Reorder the terms: 24 + -38x + 3x + 2x2 + -7x2 = -24 + -3x + 7x2 + 24 + 3x + -7x2 Combine like terms: -38x + 3x = -35x 24 + -35x + 2x2 + -7x2 = -24 + -3x + 7x2 + 24 + 3x + -7x2 Combine like terms: 2x2 + -7x2 = -5x2 24 + -35x + -5x2 = -24 + -3x + 7x2 + 24 + 3x + -7x2 Reorder the terms: 24 + -35x + -5x2 = -24 + 24 + -3x + 3x + 7x2 + -7x2 Combine like terms: -24 + 24 = 0 24 + -35x + -5x2 = 0 + -3x + 3x + 7x2 + -7x2 24 + -35x + -5x2 = -3x + 3x + 7x2 + -7x2 Combine like terms: -3x + 3x = 0 24 + -35x + -5x2 = 0 + 7x2 + -7x2 24 + -35x + -5x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 24 + -35x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -4.8 + 7x + x2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + 7x + 4.8 + x2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + 7x + x2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + 7x + x2 = 0 + 4.8 7x + x2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 7x + x2 = 4.8 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 4.8 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 4.8 + 12.25 Combine like terms: 4.8 + 12.25 = 17.05 12.25 + 7x + x2 = 17.05 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 17.05 Calculate the square root of the right side: 4.129164564 Break this problem into two subproblems by setting (x + 3.5) equal to 4.129164564 and -4.129164564.Subproblem 1
x + 3.5 = 4.129164564 Simplifying x + 3.5 = 4.129164564 Reorder the terms: 3.5 + x = 4.129164564 Solving 3.5 + x = 4.129164564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 4.129164564 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.129164564 + -3.5 x = 4.129164564 + -3.5 Combine like terms: 4.129164564 + -3.5 = 0.629164564 x = 0.629164564 Simplifying x = 0.629164564Subproblem 2
x + 3.5 = -4.129164564 Simplifying x + 3.5 = -4.129164564 Reorder the terms: 3.5 + x = -4.129164564 Solving 3.5 + x = -4.129164564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -4.129164564 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.129164564 + -3.5 x = -4.129164564 + -3.5 Combine like terms: -4.129164564 + -3.5 = -7.629164564 x = -7.629164564 Simplifying x = -7.629164564Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.629164564, -7.629164564}
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