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Simplifying 4x2 + -76x + 225 = 0 Reorder the terms: 225 + -76x + 4x2 = 0 Solving 225 + -76x + 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'. 56.25 + -19x + x2 = 0 Move the constant term to the right: Add '-56.25' to each side of the equation. 56.25 + -19x + -56.25 + x2 = 0 + -56.25 Reorder the terms: 56.25 + -56.25 + -19x + x2 = 0 + -56.25 Combine like terms: 56.25 + -56.25 = 0.00 0.00 + -19x + x2 = 0 + -56.25 -19x + x2 = 0 + -56.25 Combine like terms: 0 + -56.25 = -56.25 -19x + x2 = -56.25 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -56.25 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -56.25 + 90.25 Combine like terms: -56.25 + 90.25 = 34 90.25 + -19x + x2 = 34 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + -9.5) equal to 5.830951895 and -5.830951895.Subproblem 1
x + -9.5 = 5.830951895 Simplifying x + -9.5 = 5.830951895 Reorder the terms: -9.5 + x = 5.830951895 Solving -9.5 + x = 5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 5.830951895 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 5.830951895 + 9.5 x = 5.830951895 + 9.5 Combine like terms: 5.830951895 + 9.5 = 15.330951895 x = 15.330951895 Simplifying x = 15.330951895Subproblem 2
x + -9.5 = -5.830951895 Simplifying x + -9.5 = -5.830951895 Reorder the terms: -9.5 + x = -5.830951895 Solving -9.5 + x = -5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -5.830951895 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -5.830951895 + 9.5 x = -5.830951895 + 9.5 Combine like terms: -5.830951895 + 9.5 = 3.669048105 x = 3.669048105 Simplifying x = 3.669048105Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.330951895, 3.669048105}
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