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Simplifying 4.6x = 54 + -1x2 Solving 4.6x = 54 + -1x2 Solving for variable 'x'. Reorder the terms: -54 + 4.6x + x2 = 54 + -1x2 + -54 + x2 Reorder the terms: -54 + 4.6x + x2 = 54 + -54 + -1x2 + x2 Combine like terms: 54 + -54 = 0 -54 + 4.6x + x2 = 0 + -1x2 + x2 -54 + 4.6x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -54 + 4.6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + 4.6x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 4.6x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 4.6x + x2 = 0 + 54 4.6x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 4.6x + x2 = 54 The x term is 4.6x. Take half its coefficient (2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. 4.6x + 5.29 + x2 = 54 + 5.29 Reorder the terms: 5.29 + 4.6x + x2 = 54 + 5.29 Combine like terms: 54 + 5.29 = 59.29 5.29 + 4.6x + x2 = 59.29 Factor a perfect square on the left side: (x + 2.3)(x + 2.3) = 59.29 Calculate the square root of the right side: 7.7 Break this problem into two subproblems by setting (x + 2.3) equal to 7.7 and -7.7.Subproblem 1
x + 2.3 = 7.7 Simplifying x + 2.3 = 7.7 Reorder the terms: 2.3 + x = 7.7 Solving 2.3 + x = 7.7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.3' to each side of the equation. 2.3 + -2.3 + x = 7.7 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = 7.7 + -2.3 x = 7.7 + -2.3 Combine like terms: 7.7 + -2.3 = 5.4 x = 5.4 Simplifying x = 5.4Subproblem 2
x + 2.3 = -7.7 Simplifying x + 2.3 = -7.7 Reorder the terms: 2.3 + x = -7.7 Solving 2.3 + x = -7.7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.3' to each side of the equation. 2.3 + -2.3 + x = -7.7 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = -7.7 + -2.3 x = -7.7 + -2.3 Combine like terms: -7.7 + -2.3 = -10 x = -10 Simplifying x = -10Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.4, -10}
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