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Simplifying 4x2 + -15x + 1 = 5x + 8 Reorder the terms: 1 + -15x + 4x2 = 5x + 8 Reorder the terms: 1 + -15x + 4x2 = 8 + 5x Solving 1 + -15x + 4x2 = 8 + 5x Solving for variable 'x'. Reorder the terms: 1 + -8 + -15x + -5x + 4x2 = 8 + 5x + -8 + -5x Combine like terms: 1 + -8 = -7 -7 + -15x + -5x + 4x2 = 8 + 5x + -8 + -5x Combine like terms: -15x + -5x = -20x -7 + -20x + 4x2 = 8 + 5x + -8 + -5x Reorder the terms: -7 + -20x + 4x2 = 8 + -8 + 5x + -5x Combine like terms: 8 + -8 = 0 -7 + -20x + 4x2 = 0 + 5x + -5x -7 + -20x + 4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -7 + -20x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + -5x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -5x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -5x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -5x + x2 = 0 + 1.75 -5x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -5x + x2 = 1.75 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 = 1.75 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 1.75 + 6.25 Combine like terms: 1.75 + 6.25 = 8 6.25 + -5x + x2 = 8 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + -2.5) equal to 2.828427125 and -2.828427125.Subproblem 1
x + -2.5 = 2.828427125 Simplifying x + -2.5 = 2.828427125 Reorder the terms: -2.5 + x = 2.828427125 Solving -2.5 + x = 2.828427125 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 = 2.828427125 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.828427125 + 2.5 x = 2.828427125 + 2.5 Combine like terms: 2.828427125 + 2.5 = 5.328427125 x = 5.328427125 Simplifying x = 5.328427125Subproblem 2
x + -2.5 = -2.828427125 Simplifying x + -2.5 = -2.828427125 Reorder the terms: -2.5 + x = -2.828427125 Solving -2.5 + x = -2.828427125 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 = -2.828427125 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.828427125 + 2.5 x = -2.828427125 + 2.5 Combine like terms: -2.828427125 + 2.5 = -0.328427125 x = -0.328427125 Simplifying x = -0.328427125Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.328427125, -0.328427125}
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