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Simplifying x(x) + -1.33x + -6.67 = 0 Multiply x * x x2 + -1.33x + -6.67 = 0 Reorder the terms: -6.67 + -1.33x + x2 = 0 Solving -6.67 + -1.33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6.67' to each side of the equation. -6.67 + -1.33x + 6.67 + x2 = 0 + 6.67 Reorder the terms: -6.67 + 6.67 + -1.33x + x2 = 0 + 6.67 Combine like terms: -6.67 + 6.67 = 0.00 0.00 + -1.33x + x2 = 0 + 6.67 -1.33x + x2 = 0 + 6.67 Combine like terms: 0 + 6.67 = 6.67 -1.33x + x2 = 6.67 The x term is -1.33x. Take half its coefficient (-0.665). Square it (0.442225) and add it to both sides. Add '0.442225' to each side of the equation. -1.33x + 0.442225 + x2 = 6.67 + 0.442225 Reorder the terms: 0.442225 + -1.33x + x2 = 6.67 + 0.442225 Combine like terms: 6.67 + 0.442225 = 7.112225 0.442225 + -1.33x + x2 = 7.112225 Factor a perfect square on the left side: (x + -0.665)(x + -0.665) = 7.112225 Calculate the square root of the right side: 2.666875513 Break this problem into two subproblems by setting (x + -0.665) equal to 2.666875513 and -2.666875513.Subproblem 1
x + -0.665 = 2.666875513 Simplifying x + -0.665 = 2.666875513 Reorder the terms: -0.665 + x = 2.666875513 Solving -0.665 + x = 2.666875513 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.665' to each side of the equation. -0.665 + 0.665 + x = 2.666875513 + 0.665 Combine like terms: -0.665 + 0.665 = 0.000 0.000 + x = 2.666875513 + 0.665 x = 2.666875513 + 0.665 Combine like terms: 2.666875513 + 0.665 = 3.331875513 x = 3.331875513 Simplifying x = 3.331875513Subproblem 2
x + -0.665 = -2.666875513 Simplifying x + -0.665 = -2.666875513 Reorder the terms: -0.665 + x = -2.666875513 Solving -0.665 + x = -2.666875513 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.665' to each side of the equation. -0.665 + 0.665 + x = -2.666875513 + 0.665 Combine like terms: -0.665 + 0.665 = 0.000 0.000 + x = -2.666875513 + 0.665 x = -2.666875513 + 0.665 Combine like terms: -2.666875513 + 0.665 = -2.001875513 x = -2.001875513 Simplifying x = -2.001875513Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.331875513, -2.001875513}
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