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Simplifying 5x2 + 44x + -4 = 0 Reorder the terms: -4 + 44x + 5x2 = 0 Solving -4 + 44x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + 8.8x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 8.8x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 8.8x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 8.8x + x2 = 0 + 0.8 8.8x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 8.8x + x2 = 0.8 The x term is 8.8x. Take half its coefficient (4.4). Square it (19.36) and add it to both sides. Add '19.36' to each side of the equation. 8.8x + 19.36 + x2 = 0.8 + 19.36 Reorder the terms: 19.36 + 8.8x + x2 = 0.8 + 19.36 Combine like terms: 0.8 + 19.36 = 20.16 19.36 + 8.8x + x2 = 20.16 Factor a perfect square on the left side: (x + 4.4)(x + 4.4) = 20.16 Calculate the square root of the right side: 4.489988864 Break this problem into two subproblems by setting (x + 4.4) equal to 4.489988864 and -4.489988864.Subproblem 1
x + 4.4 = 4.489988864 Simplifying x + 4.4 = 4.489988864 Reorder the terms: 4.4 + x = 4.489988864 Solving 4.4 + x = 4.489988864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.4' to each side of the equation. 4.4 + -4.4 + x = 4.489988864 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + x = 4.489988864 + -4.4 x = 4.489988864 + -4.4 Combine like terms: 4.489988864 + -4.4 = 0.089988864 x = 0.089988864 Simplifying x = 0.089988864Subproblem 2
x + 4.4 = -4.489988864 Simplifying x + 4.4 = -4.489988864 Reorder the terms: 4.4 + x = -4.489988864 Solving 4.4 + x = -4.489988864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.4' to each side of the equation. 4.4 + -4.4 + x = -4.489988864 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + x = -4.489988864 + -4.4 x = -4.489988864 + -4.4 Combine like terms: -4.489988864 + -4.4 = -8.889988864 x = -8.889988864 Simplifying x = -8.889988864Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.089988864, -8.889988864}
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