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Simplifying 4x + 13 = x2 + 3x + 4 Reorder the terms: 13 + 4x = x2 + 3x + 4 Reorder the terms: 13 + 4x = 4 + 3x + x2 Solving 13 + 4x = 4 + 3x + x2 Solving for variable 'x'. Reorder the terms: 13 + -4 + 4x + -3x + -1x2 = 4 + 3x + x2 + -4 + -3x + -1x2 Combine like terms: 13 + -4 = 9 9 + 4x + -3x + -1x2 = 4 + 3x + x2 + -4 + -3x + -1x2 Combine like terms: 4x + -3x = 1x 9 + 1x + -1x2 = 4 + 3x + x2 + -4 + -3x + -1x2 Reorder the terms: 9 + 1x + -1x2 = 4 + -4 + 3x + -3x + x2 + -1x2 Combine like terms: 4 + -4 = 0 9 + 1x + -1x2 = 0 + 3x + -3x + x2 + -1x2 9 + 1x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 9 + 1x + -1x2 = 0 + x2 + -1x2 9 + 1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 9 + 1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + -1x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -1x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -1x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x + x2 = 0 + 9 -1x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -1x + x2 = 9 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 9 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 9 + 0.25 Combine like terms: 9 + 0.25 = 9.25 0.25 + -1x + x2 = 9.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x + -0.5) equal to 3.041381265 and -3.041381265.Subproblem 1
x + -0.5 = 3.041381265 Simplifying x + -0.5 = 3.041381265 Reorder the terms: -0.5 + x = 3.041381265 Solving -0.5 + x = 3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3.041381265 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.041381265 + 0.5 x = 3.041381265 + 0.5 Combine like terms: 3.041381265 + 0.5 = 3.541381265 x = 3.541381265 Simplifying x = 3.541381265Subproblem 2
x + -0.5 = -3.041381265 Simplifying x + -0.5 = -3.041381265 Reorder the terms: -0.5 + x = -3.041381265 Solving -0.5 + x = -3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3.041381265 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.041381265 + 0.5 x = -3.041381265 + 0.5 Combine like terms: -3.041381265 + 0.5 = -2.541381265 x = -2.541381265 Simplifying x = -2.541381265Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.541381265, -2.541381265}
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