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Simplifying 4x2 + 5x + 2 = 175 Reorder the terms: 2 + 5x + 4x2 = 175 Solving 2 + 5x + 4x2 = 175 Solving for variable 'x'. Reorder the terms: 2 + -175 + 5x + 4x2 = 175 + -175 Combine like terms: 2 + -175 = -173 -173 + 5x + 4x2 = 175 + -175 Combine like terms: 175 + -175 = 0 -173 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -43.25 + 1.25x + x2 = 0 Move the constant term to the right: Add '43.25' to each side of the equation. -43.25 + 1.25x + 43.25 + x2 = 0 + 43.25 Reorder the terms: -43.25 + 43.25 + 1.25x + x2 = 0 + 43.25 Combine like terms: -43.25 + 43.25 = 0.00 0.00 + 1.25x + x2 = 0 + 43.25 1.25x + x2 = 0 + 43.25 Combine like terms: 0 + 43.25 = 43.25 1.25x + x2 = 43.25 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 43.25 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 43.25 + 0.390625 Combine like terms: 43.25 + 0.390625 = 43.640625 0.390625 + 1.25x + x2 = 43.640625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 43.640625 Calculate the square root of the right side: 6.606105131 Break this problem into two subproblems by setting (x + 0.625) equal to 6.606105131 and -6.606105131.Subproblem 1
x + 0.625 = 6.606105131 Simplifying x + 0.625 = 6.606105131 Reorder the terms: 0.625 + x = 6.606105131 Solving 0.625 + x = 6.606105131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 6.606105131 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 6.606105131 + -0.625 x = 6.606105131 + -0.625 Combine like terms: 6.606105131 + -0.625 = 5.981105131 x = 5.981105131 Simplifying x = 5.981105131Subproblem 2
x + 0.625 = -6.606105131 Simplifying x + 0.625 = -6.606105131 Reorder the terms: 0.625 + x = -6.606105131 Solving 0.625 + x = -6.606105131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -6.606105131 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -6.606105131 + -0.625 x = -6.606105131 + -0.625 Combine like terms: -6.606105131 + -0.625 = -7.231105131 x = -7.231105131 Simplifying x = -7.231105131Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.981105131, -7.231105131}
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