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Simplifying (-4x2) + (40x) + 25 = 20 Reorder the terms: 25 + (40x) + (-4x2) = 20 Solving 25 + (40x) + (-4x2) = 20 Solving for variable 'x'. Reorder the terms: 25 + -20 + (40x) + (-4x2) = 20 + -20 Combine like terms: 25 + -20 = 5 5 + (40x) + (-4x2) = 20 + -20 Combine like terms: 20 + -20 = 0 5 + (40x) + (-4x2) = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.25 + (-10x) + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + (-10x) + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + (-10x) + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + (-10x) + x2 = 0 + 1.25 (-10x) + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 (-10x) + x2 = 1.25 The x term is (-10x). Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. (-10x) + 25 + x2 = 1.25 + 25 Reorder the terms: 25 + (-10x) + x2 = 1.25 + 25 Combine like terms: 1.25 + 25 = 26.25 25 + (-10x) + x2 = 26.25 Factor a perfect square on the left side: ((x) + -5)((x) + -5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting ((x) + -5) equal to 5.123475383 and -5.123475383.Subproblem 1
(x) + -5 = 5.123475383 Simplifying (x) + -5 = 5.123475383 x + -5 = 5.123475383 Reorder the terms: -5 + x = 5.123475383 Solving -5 + x = 5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.123475383 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.123475383 + 5 x = 5.123475383 + 5 Combine like terms: 5.123475383 + 5 = 10.123475383 x = 10.123475383 Simplifying x = 10.123475383Subproblem 2
(x) + -5 = -5.123475383 Simplifying (x) + -5 = -5.123475383 x + -5 = -5.123475383 Reorder the terms: -5 + x = -5.123475383 Solving -5 + x = -5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.123475383 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.123475383 + 5 x = -5.123475383 + 5 Combine like terms: -5.123475383 + 5 = -0.123475383 x = -0.123475383 Simplifying x = -0.123475383Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.123475383, -0.123475383}
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