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Simplifying 10x2 + -25x + 4 = 0 Reorder the terms: 4 + -25x + 10x2 = 0 Solving 4 + -25x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.4 + -2.5x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -2.5x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -2.5x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -2.5x + x2 = 0 + -0.4 -2.5x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -2.5x + x2 = -0.4 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -0.4 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -0.4 + 1.5625 Combine like terms: -0.4 + 1.5625 = 1.1625 1.5625 + -2.5x + x2 = 1.1625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 1.1625 Calculate the square root of the right side: 1.078192933 Break this problem into two subproblems by setting (x + -1.25) equal to 1.078192933 and -1.078192933.Subproblem 1
x + -1.25 = 1.078192933 Simplifying x + -1.25 = 1.078192933 Reorder the terms: -1.25 + x = 1.078192933 Solving -1.25 + x = 1.078192933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.078192933 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.078192933 + 1.25 x = 1.078192933 + 1.25 Combine like terms: 1.078192933 + 1.25 = 2.328192933 x = 2.328192933 Simplifying x = 2.328192933Subproblem 2
x + -1.25 = -1.078192933 Simplifying x + -1.25 = -1.078192933 Reorder the terms: -1.25 + x = -1.078192933 Solving -1.25 + x = -1.078192933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.078192933 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.078192933 + 1.25 x = -1.078192933 + 1.25 Combine like terms: -1.078192933 + 1.25 = 0.171807067 x = 0.171807067 Simplifying x = 0.171807067Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.328192933, 0.171807067}
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