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Simplifying 4x2 + 17x + 7 = 5 Reorder the terms: 7 + 17x + 4x2 = 5 Solving 7 + 17x + 4x2 = 5 Solving for variable 'x'. Reorder the terms: 7 + -5 + 17x + 4x2 = 5 + -5 Combine like terms: 7 + -5 = 2 2 + 17x + 4x2 = 5 + -5 Combine like terms: 5 + -5 = 0 2 + 17x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + 4.25x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 4.25x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 4.25x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 4.25x + x2 = 0 + -0.5 4.25x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 4.25x + x2 = -0.5 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = -0.5 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = -0.5 + 4.515625 Combine like terms: -0.5 + 4.515625 = 4.015625 4.515625 + 4.25x + x2 = 4.015625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 4.015625 Calculate the square root of the right side: 2.003902443 Break this problem into two subproblems by setting (x + 2.125) equal to 2.003902443 and -2.003902443.Subproblem 1
x + 2.125 = 2.003902443 Simplifying x + 2.125 = 2.003902443 Reorder the terms: 2.125 + x = 2.003902443 Solving 2.125 + x = 2.003902443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 2.003902443 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 2.003902443 + -2.125 x = 2.003902443 + -2.125 Combine like terms: 2.003902443 + -2.125 = -0.121097557 x = -0.121097557 Simplifying x = -0.121097557Subproblem 2
x + 2.125 = -2.003902443 Simplifying x + 2.125 = -2.003902443 Reorder the terms: 2.125 + x = -2.003902443 Solving 2.125 + x = -2.003902443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -2.003902443 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -2.003902443 + -2.125 x = -2.003902443 + -2.125 Combine like terms: -2.003902443 + -2.125 = -4.128902443 x = -4.128902443 Simplifying x = -4.128902443Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.121097557, -4.128902443}
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