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Simplifying 5x2 + 28x + -1 = 0 Reorder the terms: -1 + 28x + 5x2 = 0 Solving -1 + 28x + 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'. -0.2 + 5.6x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 5.6x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 5.6x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 5.6x + x2 = 0 + 0.2 5.6x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 5.6x + x2 = 0.2 The x term is 5.6x. Take half its coefficient (2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. 5.6x + 7.84 + x2 = 0.2 + 7.84 Reorder the terms: 7.84 + 5.6x + x2 = 0.2 + 7.84 Combine like terms: 0.2 + 7.84 = 8.04 7.84 + 5.6x + x2 = 8.04 Factor a perfect square on the left side: (x + 2.8)(x + 2.8) = 8.04 Calculate the square root of the right side: 2.835489376 Break this problem into two subproblems by setting (x + 2.8) equal to 2.835489376 and -2.835489376.Subproblem 1
x + 2.8 = 2.835489376 Simplifying x + 2.8 = 2.835489376 Reorder the terms: 2.8 + x = 2.835489376 Solving 2.8 + x = 2.835489376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.8' to each side of the equation. 2.8 + -2.8 + x = 2.835489376 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = 2.835489376 + -2.8 x = 2.835489376 + -2.8 Combine like terms: 2.835489376 + -2.8 = 0.035489376 x = 0.035489376 Simplifying x = 0.035489376Subproblem 2
x + 2.8 = -2.835489376 Simplifying x + 2.8 = -2.835489376 Reorder the terms: 2.8 + x = -2.835489376 Solving 2.8 + x = -2.835489376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.8' to each side of the equation. 2.8 + -2.8 + x = -2.835489376 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = -2.835489376 + -2.8 x = -2.835489376 + -2.8 Combine like terms: -2.835489376 + -2.8 = -5.635489376 x = -5.635489376 Simplifying x = -5.635489376Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.035489376, -5.635489376}
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