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Simplifying 4x2 = 7x + 13 Reorder the terms: 4x2 = 13 + 7x Solving 4x2 = 13 + 7x Solving for variable 'x'. Reorder the terms: -13 + -7x + 4x2 = 13 + 7x + -13 + -7x Reorder the terms: -13 + -7x + 4x2 = 13 + -13 + 7x + -7x Combine like terms: 13 + -13 = 0 -13 + -7x + 4x2 = 0 + 7x + -7x -13 + -7x + 4x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -13 + -7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.25 + -1.75x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + -1.75x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + -1.75x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + -1.75x + x2 = 0 + 3.25 -1.75x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 -1.75x + x2 = 3.25 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = 3.25 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 3.25 + 0.765625 Combine like terms: 3.25 + 0.765625 = 4.015625 0.765625 + -1.75x + x2 = 4.015625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 4.015625 Calculate the square root of the right side: 2.003902443 Break this problem into two subproblems by setting (x + -0.875) equal to 2.003902443 and -2.003902443.Subproblem 1
x + -0.875 = 2.003902443 Simplifying x + -0.875 = 2.003902443 Reorder the terms: -0.875 + x = 2.003902443 Solving -0.875 + x = 2.003902443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 2.003902443 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 2.003902443 + 0.875 x = 2.003902443 + 0.875 Combine like terms: 2.003902443 + 0.875 = 2.878902443 x = 2.878902443 Simplifying x = 2.878902443Subproblem 2
x + -0.875 = -2.003902443 Simplifying x + -0.875 = -2.003902443 Reorder the terms: -0.875 + x = -2.003902443 Solving -0.875 + x = -2.003902443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -2.003902443 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -2.003902443 + 0.875 x = -2.003902443 + 0.875 Combine like terms: -2.003902443 + 0.875 = -1.128902443 x = -1.128902443 Simplifying x = -1.128902443Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.878902443, -1.128902443}
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