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Simplifying 4.6x = 4 + -1x2 Solving 4.6x = 4 + -1x2 Solving for variable 'x'. Reorder the terms: -4 + 4.6x + x2 = 4 + -1x2 + -4 + x2 Reorder the terms: -4 + 4.6x + x2 = 4 + -4 + -1x2 + x2 Combine like terms: 4 + -4 = 0 -4 + 4.6x + x2 = 0 + -1x2 + x2 -4 + 4.6x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -4 + 4.6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 4.6x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 4.6x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 4.6x + x2 = 0 + 4 4.6x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 4.6x + x2 = 4 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 = 4 + 5.29 Reorder the terms: 5.29 + 4.6x + x2 = 4 + 5.29 Combine like terms: 4 + 5.29 = 9.29 5.29 + 4.6x + x2 = 9.29 Factor a perfect square on the left side: (x + 2.3)(x + 2.3) = 9.29 Calculate the square root of the right side: 3.047950131 Break this problem into two subproblems by setting (x + 2.3) equal to 3.047950131 and -3.047950131.Subproblem 1
x + 2.3 = 3.047950131 Simplifying x + 2.3 = 3.047950131 Reorder the terms: 2.3 + x = 3.047950131 Solving 2.3 + x = 3.047950131 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 = 3.047950131 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = 3.047950131 + -2.3 x = 3.047950131 + -2.3 Combine like terms: 3.047950131 + -2.3 = 0.747950131 x = 0.747950131 Simplifying x = 0.747950131Subproblem 2
x + 2.3 = -3.047950131 Simplifying x + 2.3 = -3.047950131 Reorder the terms: 2.3 + x = -3.047950131 Solving 2.3 + x = -3.047950131 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 = -3.047950131 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = -3.047950131 + -2.3 x = -3.047950131 + -2.3 Combine like terms: -3.047950131 + -2.3 = -5.347950131 x = -5.347950131 Simplifying x = -5.347950131Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.747950131, -5.347950131}
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