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Simplifying 3x2 + -31x + 36 = 4x2 + -59x + 15 Reorder the terms: 36 + -31x + 3x2 = 4x2 + -59x + 15 Reorder the terms: 36 + -31x + 3x2 = 15 + -59x + 4x2 Solving 36 + -31x + 3x2 = 15 + -59x + 4x2 Solving for variable 'x'. Reorder the terms: 36 + -15 + -31x + 59x + 3x2 + -4x2 = 15 + -59x + 4x2 + -15 + 59x + -4x2 Combine like terms: 36 + -15 = 21 21 + -31x + 59x + 3x2 + -4x2 = 15 + -59x + 4x2 + -15 + 59x + -4x2 Combine like terms: -31x + 59x = 28x 21 + 28x + 3x2 + -4x2 = 15 + -59x + 4x2 + -15 + 59x + -4x2 Combine like terms: 3x2 + -4x2 = -1x2 21 + 28x + -1x2 = 15 + -59x + 4x2 + -15 + 59x + -4x2 Reorder the terms: 21 + 28x + -1x2 = 15 + -15 + -59x + 59x + 4x2 + -4x2 Combine like terms: 15 + -15 = 0 21 + 28x + -1x2 = 0 + -59x + 59x + 4x2 + -4x2 21 + 28x + -1x2 = -59x + 59x + 4x2 + -4x2 Combine like terms: -59x + 59x = 0 21 + 28x + -1x2 = 0 + 4x2 + -4x2 21 + 28x + -1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 21 + 28x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + -28x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -28x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -28x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -28x + x2 = 0 + 21 -28x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -28x + x2 = 21 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = 21 + 196 Reorder the terms: 196 + -28x + x2 = 21 + 196 Combine like terms: 21 + 196 = 217 196 + -28x + x2 = 217 Factor a perfect square on the left side: (x + -14)(x + -14) = 217 Calculate the square root of the right side: 14.730919863 Break this problem into two subproblems by setting (x + -14) equal to 14.730919863 and -14.730919863.Subproblem 1
x + -14 = 14.730919863 Simplifying x + -14 = 14.730919863 Reorder the terms: -14 + x = 14.730919863 Solving -14 + x = 14.730919863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 14.730919863 + 14 Combine like terms: -14 + 14 = 0 0 + x = 14.730919863 + 14 x = 14.730919863 + 14 Combine like terms: 14.730919863 + 14 = 28.730919863 x = 28.730919863 Simplifying x = 28.730919863Subproblem 2
x + -14 = -14.730919863 Simplifying x + -14 = -14.730919863 Reorder the terms: -14 + x = -14.730919863 Solving -14 + x = -14.730919863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -14.730919863 + 14 Combine like terms: -14 + 14 = 0 0 + x = -14.730919863 + 14 x = -14.730919863 + 14 Combine like terms: -14.730919863 + 14 = -0.730919863 x = -0.730919863 Simplifying x = -0.730919863Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.730919863, -0.730919863}
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