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Simplifying x2(0.5) + 0.63x = 2 Reorder the terms for easier multiplication: 0.5x2 + 0.63x = 2 Reorder the terms: 0.63x + 0.5x2 = 2 Solving 0.63x + 0.5x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 0.63x + 0.5x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 0.63x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -4 + 1.26x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 1.26x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 1.26x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 1.26x + x2 = 0 + 4 1.26x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 1.26x + x2 = 4 The x term is 1.26x. Take half its coefficient (0.63). Square it (0.3969) and add it to both sides. Add '0.3969' to each side of the equation. 1.26x + 0.3969 + x2 = 4 + 0.3969 Reorder the terms: 0.3969 + 1.26x + x2 = 4 + 0.3969 Combine like terms: 4 + 0.3969 = 4.3969 0.3969 + 1.26x + x2 = 4.3969 Factor a perfect square on the left side: (x + 0.63)(x + 0.63) = 4.3969 Calculate the square root of the right side: 2.096878633 Break this problem into two subproblems by setting (x + 0.63) equal to 2.096878633 and -2.096878633.Subproblem 1
x + 0.63 = 2.096878633 Simplifying x + 0.63 = 2.096878633 Reorder the terms: 0.63 + x = 2.096878633 Solving 0.63 + x = 2.096878633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.63' to each side of the equation. 0.63 + -0.63 + x = 2.096878633 + -0.63 Combine like terms: 0.63 + -0.63 = 0.00 0.00 + x = 2.096878633 + -0.63 x = 2.096878633 + -0.63 Combine like terms: 2.096878633 + -0.63 = 1.466878633 x = 1.466878633 Simplifying x = 1.466878633Subproblem 2
x + 0.63 = -2.096878633 Simplifying x + 0.63 = -2.096878633 Reorder the terms: 0.63 + x = -2.096878633 Solving 0.63 + x = -2.096878633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.63' to each side of the equation. 0.63 + -0.63 + x = -2.096878633 + -0.63 Combine like terms: 0.63 + -0.63 = 0.00 0.00 + x = -2.096878633 + -0.63 x = -2.096878633 + -0.63 Combine like terms: -2.096878633 + -0.63 = -2.726878633 x = -2.726878633 Simplifying x = -2.726878633Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.466878633, -2.726878633}
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