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Simplifying -4.9x2 + 6.84x + 33 = 0 Reorder the terms: 33 + 6.84x + -4.9x2 = 0 Solving 33 + 6.84x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -6.734693878 + -1.395918367x + x2 = 0 Move the constant term to the right: Add '6.734693878' to each side of the equation. -6.734693878 + -1.395918367x + 6.734693878 + x2 = 0 + 6.734693878 Reorder the terms: -6.734693878 + 6.734693878 + -1.395918367x + x2 = 0 + 6.734693878 Combine like terms: -6.734693878 + 6.734693878 = 0.000000000 0.000000000 + -1.395918367x + x2 = 0 + 6.734693878 -1.395918367x + x2 = 0 + 6.734693878 Combine like terms: 0 + 6.734693878 = 6.734693878 -1.395918367x + x2 = 6.734693878 The x term is -1.395918367x. Take half its coefficient (-0.6979591835). Square it (0.4871470218) and add it to both sides. Add '0.4871470218' to each side of the equation. -1.395918367x + 0.4871470218 + x2 = 6.734693878 + 0.4871470218 Reorder the terms: 0.4871470218 + -1.395918367x + x2 = 6.734693878 + 0.4871470218 Combine like terms: 6.734693878 + 0.4871470218 = 7.2218408998 0.4871470218 + -1.395918367x + x2 = 7.2218408998 Factor a perfect square on the left side: (x + -0.6979591835)(x + -0.6979591835) = 7.2218408998 Calculate the square root of the right side: 2.687348303 Break this problem into two subproblems by setting (x + -0.6979591835) equal to 2.687348303 and -2.687348303.Subproblem 1
x + -0.6979591835 = 2.687348303 Simplifying x + -0.6979591835 = 2.687348303 Reorder the terms: -0.6979591835 + x = 2.687348303 Solving -0.6979591835 + x = 2.687348303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6979591835' to each side of the equation. -0.6979591835 + 0.6979591835 + x = 2.687348303 + 0.6979591835 Combine like terms: -0.6979591835 + 0.6979591835 = 0.0000000000 0.0000000000 + x = 2.687348303 + 0.6979591835 x = 2.687348303 + 0.6979591835 Combine like terms: 2.687348303 + 0.6979591835 = 3.3853074865 x = 3.3853074865 Simplifying x = 3.3853074865Subproblem 2
x + -0.6979591835 = -2.687348303 Simplifying x + -0.6979591835 = -2.687348303 Reorder the terms: -0.6979591835 + x = -2.687348303 Solving -0.6979591835 + x = -2.687348303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6979591835' to each side of the equation. -0.6979591835 + 0.6979591835 + x = -2.687348303 + 0.6979591835 Combine like terms: -0.6979591835 + 0.6979591835 = 0.0000000000 0.0000000000 + x = -2.687348303 + 0.6979591835 x = -2.687348303 + 0.6979591835 Combine like terms: -2.687348303 + 0.6979591835 = -1.9893891195 x = -1.9893891195 Simplifying x = -1.9893891195Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.3853074865, -1.9893891195}
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