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Simplifying -4x2 + 21x = x + 13 Reorder the terms: 21x + -4x2 = x + 13 Reorder the terms: 21x + -4x2 = 13 + x Solving 21x + -4x2 = 13 + x Solving for variable 'x'. Reorder the terms: -13 + 21x + -1x + -4x2 = 13 + x + -13 + -1x Combine like terms: 21x + -1x = 20x -13 + 20x + -4x2 = 13 + x + -13 + -1x Reorder the terms: -13 + 20x + -4x2 = 13 + -13 + x + -1x Combine like terms: 13 + -13 = 0 -13 + 20x + -4x2 = 0 + x + -1x -13 + 20x + -4x2 = x + -1x Combine like terms: x + -1x = 0 -13 + 20x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 3.25 + -5x + x2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + -5x + -3.25 + x2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + -5x + x2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + -5x + x2 = 0 + -3.25 -5x + x2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 -5x + x2 = -3.25 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -3.25 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -3.25 + 6.25 Combine like terms: -3.25 + 6.25 = 3 6.25 + -5x + x2 = 3 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + -2.5) equal to 1.732050808 and -1.732050808.Subproblem 1
x + -2.5 = 1.732050808 Simplifying x + -2.5 = 1.732050808 Reorder the terms: -2.5 + x = 1.732050808 Solving -2.5 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.732050808 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.732050808 + 2.5 x = 1.732050808 + 2.5 Combine like terms: 1.732050808 + 2.5 = 4.232050808 x = 4.232050808 Simplifying x = 4.232050808Subproblem 2
x + -2.5 = -1.732050808 Simplifying x + -2.5 = -1.732050808 Reorder the terms: -2.5 + x = -1.732050808 Solving -2.5 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.732050808 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.732050808 + 2.5 x = -1.732050808 + 2.5 Combine like terms: -1.732050808 + 2.5 = 0.767949192 x = 0.767949192 Simplifying x = 0.767949192Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.232050808, 0.767949192}
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