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Simplifying 0.04x + -0.07x2 = -2 Solving 0.04x + -0.07x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + 0.04x + -0.07x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 0.04x + -0.07x2 = 0 Begin completing the square. Divide all terms by -0.07 the coefficient of the squared term: Divide each side by '-0.07'. -28.57142857 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '28.57142857' to each side of the equation. -28.57142857 + -0.5714285714x + 28.57142857 + x2 = 0 + 28.57142857 Reorder the terms: -28.57142857 + 28.57142857 + -0.5714285714x + x2 = 0 + 28.57142857 Combine like terms: -28.57142857 + 28.57142857 = 0.00000000 0.00000000 + -0.5714285714x + x2 = 0 + 28.57142857 -0.5714285714x + x2 = 0 + 28.57142857 Combine like terms: 0 + 28.57142857 = 28.57142857 -0.5714285714x + x2 = 28.57142857 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 28.57142857 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 28.57142857 + 0.08163265305 Combine like terms: 28.57142857 + 0.08163265305 = 28.65306122305 0.08163265305 + -0.5714285714x + x2 = 28.65306122305 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 28.65306122305 Calculate the square root of the right side: 5.352855427 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 5.352855427 and -5.352855427.Subproblem 1
x + -0.2857142857 = 5.352855427 Simplifying x + -0.2857142857 = 5.352855427 Reorder the terms: -0.2857142857 + x = 5.352855427 Solving -0.2857142857 + x = 5.352855427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 5.352855427 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 5.352855427 + 0.2857142857 x = 5.352855427 + 0.2857142857 Combine like terms: 5.352855427 + 0.2857142857 = 5.6385697127 x = 5.6385697127 Simplifying x = 5.6385697127Subproblem 2
x + -0.2857142857 = -5.352855427 Simplifying x + -0.2857142857 = -5.352855427 Reorder the terms: -0.2857142857 + x = -5.352855427 Solving -0.2857142857 + x = -5.352855427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -5.352855427 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -5.352855427 + 0.2857142857 x = -5.352855427 + 0.2857142857 Combine like terms: -5.352855427 + 0.2857142857 = -5.0671411413 x = -5.0671411413 Simplifying x = -5.0671411413Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.6385697127, -5.0671411413}
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