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Simplifying 0.67x + 0.5 = x2 Reorder the terms: 0.5 + 0.67x = x2 Solving 0.5 + 0.67x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 0.5 + 0.67x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.5 + -0.67x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.67x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.67x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.67x + x2 = 0 + 0.5 -0.67x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.67x + x2 = 0.5 The x term is -0.67x. Take half its coefficient (-0.335). Square it (0.112225) and add it to both sides. Add '0.112225' to each side of the equation. -0.67x + 0.112225 + x2 = 0.5 + 0.112225 Reorder the terms: 0.112225 + -0.67x + x2 = 0.5 + 0.112225 Combine like terms: 0.5 + 0.112225 = 0.612225 0.112225 + -0.67x + x2 = 0.612225 Factor a perfect square on the left side: (x + -0.335)(x + -0.335) = 0.612225 Calculate the square root of the right side: 0.782448081 Break this problem into two subproblems by setting (x + -0.335) equal to 0.782448081 and -0.782448081.Subproblem 1
x + -0.335 = 0.782448081 Simplifying x + -0.335 = 0.782448081 Reorder the terms: -0.335 + x = 0.782448081 Solving -0.335 + x = 0.782448081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.335' to each side of the equation. -0.335 + 0.335 + x = 0.782448081 + 0.335 Combine like terms: -0.335 + 0.335 = 0.000 0.000 + x = 0.782448081 + 0.335 x = 0.782448081 + 0.335 Combine like terms: 0.782448081 + 0.335 = 1.117448081 x = 1.117448081 Simplifying x = 1.117448081Subproblem 2
x + -0.335 = -0.782448081 Simplifying x + -0.335 = -0.782448081 Reorder the terms: -0.335 + x = -0.782448081 Solving -0.335 + x = -0.782448081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.335' to each side of the equation. -0.335 + 0.335 + x = -0.782448081 + 0.335 Combine like terms: -0.335 + 0.335 = 0.000 0.000 + x = -0.782448081 + 0.335 x = -0.782448081 + 0.335 Combine like terms: -0.782448081 + 0.335 = -0.447448081 x = -0.447448081 Simplifying x = -0.447448081Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.117448081, -0.447448081}
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