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Simplifying -4.9x2 + 6.88x + -1.25 = 0 Reorder the terms: -1.25 + 6.88x + -4.9x2 = 0 Solving -1.25 + 6.88x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 0.2551020408 + -1.404081633x + x2 = 0 Move the constant term to the right: Add '-0.2551020408' to each side of the equation. 0.2551020408 + -1.404081633x + -0.2551020408 + x2 = 0 + -0.2551020408 Reorder the terms: 0.2551020408 + -0.2551020408 + -1.404081633x + x2 = 0 + -0.2551020408 Combine like terms: 0.2551020408 + -0.2551020408 = 0.0000000000 0.0000000000 + -1.404081633x + x2 = 0 + -0.2551020408 -1.404081633x + x2 = 0 + -0.2551020408 Combine like terms: 0 + -0.2551020408 = -0.2551020408 -1.404081633x + x2 = -0.2551020408 The x term is -1.404081633x. Take half its coefficient (-0.7020408165). Square it (0.4928613080) and add it to both sides. Add '0.4928613080' to each side of the equation. -1.404081633x + 0.4928613080 + x2 = -0.2551020408 + 0.4928613080 Reorder the terms: 0.4928613080 + -1.404081633x + x2 = -0.2551020408 + 0.4928613080 Combine like terms: -0.2551020408 + 0.4928613080 = 0.2377592672 0.4928613080 + -1.404081633x + x2 = 0.2377592672 Factor a perfect square on the left side: (x + -0.7020408165)(x + -0.7020408165) = 0.2377592672 Calculate the square root of the right side: 0.487605647 Break this problem into two subproblems by setting (x + -0.7020408165) equal to 0.487605647 and -0.487605647.Subproblem 1
x + -0.7020408165 = 0.487605647 Simplifying x + -0.7020408165 = 0.487605647 Reorder the terms: -0.7020408165 + x = 0.487605647 Solving -0.7020408165 + x = 0.487605647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7020408165' to each side of the equation. -0.7020408165 + 0.7020408165 + x = 0.487605647 + 0.7020408165 Combine like terms: -0.7020408165 + 0.7020408165 = 0.0000000000 0.0000000000 + x = 0.487605647 + 0.7020408165 x = 0.487605647 + 0.7020408165 Combine like terms: 0.487605647 + 0.7020408165 = 1.1896464635 x = 1.1896464635 Simplifying x = 1.1896464635Subproblem 2
x + -0.7020408165 = -0.487605647 Simplifying x + -0.7020408165 = -0.487605647 Reorder the terms: -0.7020408165 + x = -0.487605647 Solving -0.7020408165 + x = -0.487605647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7020408165' to each side of the equation. -0.7020408165 + 0.7020408165 + x = -0.487605647 + 0.7020408165 Combine like terms: -0.7020408165 + 0.7020408165 = 0.0000000000 0.0000000000 + x = -0.487605647 + 0.7020408165 x = -0.487605647 + 0.7020408165 Combine like terms: -0.487605647 + 0.7020408165 = 0.2144351695 x = 0.2144351695 Simplifying x = 0.2144351695Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1896464635, 0.2144351695}
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