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Simplifying 4x2 + 4x + -175 = 0 Reorder the terms: -175 + 4x + 4x2 = 0 Solving -175 + 4x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -43.75 + x + x2 = 0 Move the constant term to the right: Add '43.75' to each side of the equation. -43.75 + x + 43.75 + x2 = 0 + 43.75 Reorder the terms: -43.75 + 43.75 + x + x2 = 0 + 43.75 Combine like terms: -43.75 + 43.75 = 0.00 0.00 + x + x2 = 0 + 43.75 x + x2 = 0 + 43.75 Combine like terms: 0 + 43.75 = 43.75 x + x2 = 43.75 The x term is x. 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. + 0.25 + x2 = 43.75 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 43.75 + 0.25 Combine like terms: 43.75 + 0.25 = 44 1.25 + x2 = 44 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (x + 0.5) equal to 6.633249581 and -6.633249581.Subproblem 1
x + 0.5 = 6.633249581 Simplifying x + 0.5 = 6.633249581 Reorder the terms: 0.5 + x = 6.633249581 Solving 0.5 + x = 6.633249581 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 = 6.633249581 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.633249581 + -0.5 x = 6.633249581 + -0.5 Combine like terms: 6.633249581 + -0.5 = 6.133249581 x = 6.133249581 Simplifying x = 6.133249581Subproblem 2
x + 0.5 = -6.633249581 Simplifying x + 0.5 = -6.633249581 Reorder the terms: 0.5 + x = -6.633249581 Solving 0.5 + x = -6.633249581 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 = -6.633249581 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.633249581 + -0.5 x = -6.633249581 + -0.5 Combine like terms: -6.633249581 + -0.5 = -7.133249581 x = -7.133249581 Simplifying x = -7.133249581Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.133249581, -7.133249581}
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