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Simplifying 4x2 + -0.5x + -154 = 0 Reorder the terms: -154 + -0.5x + 4x2 = 0 Solving -154 + -0.5x + 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'. -38.5 + -0.125x + x2 = 0 Move the constant term to the right: Add '38.5' to each side of the equation. -38.5 + -0.125x + 38.5 + x2 = 0 + 38.5 Reorder the terms: -38.5 + 38.5 + -0.125x + x2 = 0 + 38.5 Combine like terms: -38.5 + 38.5 = 0.0 0.0 + -0.125x + x2 = 0 + 38.5 -0.125x + x2 = 0 + 38.5 Combine like terms: 0 + 38.5 = 38.5 -0.125x + x2 = 38.5 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = 38.5 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 38.5 + 0.00390625 Combine like terms: 38.5 + 0.00390625 = 38.50390625 0.00390625 + -0.125x + x2 = 38.50390625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 38.50390625 Calculate the square root of the right side: 6.20515159 Break this problem into two subproblems by setting (x + -0.0625) equal to 6.20515159 and -6.20515159.Subproblem 1
x + -0.0625 = 6.20515159 Simplifying x + -0.0625 = 6.20515159 Reorder the terms: -0.0625 + x = 6.20515159 Solving -0.0625 + x = 6.20515159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 6.20515159 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 6.20515159 + 0.0625 x = 6.20515159 + 0.0625 Combine like terms: 6.20515159 + 0.0625 = 6.26765159 x = 6.26765159 Simplifying x = 6.26765159Subproblem 2
x + -0.0625 = -6.20515159 Simplifying x + -0.0625 = -6.20515159 Reorder the terms: -0.0625 + x = -6.20515159 Solving -0.0625 + x = -6.20515159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -6.20515159 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -6.20515159 + 0.0625 x = -6.20515159 + 0.0625 Combine like terms: -6.20515159 + 0.0625 = -6.14265159 x = -6.14265159 Simplifying x = -6.14265159Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.26765159, -6.14265159}
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