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Simplifying 5x2 + 4x + -48 = 0 Reorder the terms: -48 + 4x + 5x2 = 0 Solving -48 + 4x + 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'. -9.6 + 0.8x + x2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + 0.8x + 9.6 + x2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + 0.8x + x2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + 0.8x + x2 = 0 + 9.6 0.8x + x2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 0.8x + x2 = 9.6 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 9.6 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 9.6 + 0.16 Combine like terms: 9.6 + 0.16 = 9.76 0.16 + 0.8x + x2 = 9.76 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 9.76 Calculate the square root of the right side: 3.12409987 Break this problem into two subproblems by setting (x + 0.4) equal to 3.12409987 and -3.12409987.Subproblem 1
x + 0.4 = 3.12409987 Simplifying x + 0.4 = 3.12409987 Reorder the terms: 0.4 + x = 3.12409987 Solving 0.4 + x = 3.12409987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 3.12409987 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 3.12409987 + -0.4 x = 3.12409987 + -0.4 Combine like terms: 3.12409987 + -0.4 = 2.72409987 x = 2.72409987 Simplifying x = 2.72409987Subproblem 2
x + 0.4 = -3.12409987 Simplifying x + 0.4 = -3.12409987 Reorder the terms: 0.4 + x = -3.12409987 Solving 0.4 + x = -3.12409987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -3.12409987 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -3.12409987 + -0.4 x = -3.12409987 + -0.4 Combine like terms: -3.12409987 + -0.4 = -3.52409987 x = -3.52409987 Simplifying x = -3.52409987Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.72409987, -3.52409987}
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