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Simplifying 5x2 + 9x + -56 = 0 Reorder the terms: -56 + 9x + 5x2 = 0 Solving -56 + 9x + 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'. -11.2 + 1.8x + x2 = 0 Move the constant term to the right: Add '11.2' to each side of the equation. -11.2 + 1.8x + 11.2 + x2 = 0 + 11.2 Reorder the terms: -11.2 + 11.2 + 1.8x + x2 = 0 + 11.2 Combine like terms: -11.2 + 11.2 = 0.0 0.0 + 1.8x + x2 = 0 + 11.2 1.8x + x2 = 0 + 11.2 Combine like terms: 0 + 11.2 = 11.2 1.8x + x2 = 11.2 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = 11.2 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 11.2 + 0.81 Combine like terms: 11.2 + 0.81 = 12.01 0.81 + 1.8x + x2 = 12.01 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 12.01 Calculate the square root of the right side: 3.46554469 Break this problem into two subproblems by setting (x + 0.9) equal to 3.46554469 and -3.46554469.Subproblem 1
x + 0.9 = 3.46554469 Simplifying x + 0.9 = 3.46554469 Reorder the terms: 0.9 + x = 3.46554469 Solving 0.9 + x = 3.46554469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 3.46554469 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 3.46554469 + -0.9 x = 3.46554469 + -0.9 Combine like terms: 3.46554469 + -0.9 = 2.56554469 x = 2.56554469 Simplifying x = 2.56554469Subproblem 2
x + 0.9 = -3.46554469 Simplifying x + 0.9 = -3.46554469 Reorder the terms: 0.9 + x = -3.46554469 Solving 0.9 + x = -3.46554469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -3.46554469 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -3.46554469 + -0.9 x = -3.46554469 + -0.9 Combine like terms: -3.46554469 + -0.9 = -4.36554469 x = -4.36554469 Simplifying x = -4.36554469Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.56554469, -4.36554469}
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