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Simplifying 0.56x2 + 112x + 56 = 0 Reorder the terms: 56 + 112x + 0.56x2 = 0 Solving 56 + 112x + 0.56x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.56 the coefficient of the squared term: Divide each side by '0.56'. 100 + 200x + x2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + 200x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + 200x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + 200x + x2 = 0 + -100 200x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 200x + x2 = -100 The x term is 200x. Take half its coefficient (100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. 200x + 10000 + x2 = -100 + 10000 Reorder the terms: 10000 + 200x + x2 = -100 + 10000 Combine like terms: -100 + 10000 = 9900 10000 + 200x + x2 = 9900 Factor a perfect square on the left side: (x + 100)(x + 100) = 9900 Calculate the square root of the right side: 99.498743711 Break this problem into two subproblems by setting (x + 100) equal to 99.498743711 and -99.498743711.Subproblem 1
x + 100 = 99.498743711 Simplifying x + 100 = 99.498743711 Reorder the terms: 100 + x = 99.498743711 Solving 100 + x = 99.498743711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = 99.498743711 + -100 Combine like terms: 100 + -100 = 0 0 + x = 99.498743711 + -100 x = 99.498743711 + -100 Combine like terms: 99.498743711 + -100 = -0.501256289 x = -0.501256289 Simplifying x = -0.501256289Subproblem 2
x + 100 = -99.498743711 Simplifying x + 100 = -99.498743711 Reorder the terms: 100 + x = -99.498743711 Solving 100 + x = -99.498743711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = -99.498743711 + -100 Combine like terms: 100 + -100 = 0 0 + x = -99.498743711 + -100 x = -99.498743711 + -100 Combine like terms: -99.498743711 + -100 = -199.498743711 x = -199.498743711 Simplifying x = -199.498743711Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.501256289, -199.498743711}
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