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Simplifying 1.5x + 0.25x(x + -2) = 10 Reorder the terms: 1.5x + 0.25x(-2 + x) = 10 1.5x + (-2 * 0.25x + x * 0.25x) = 10 1.5x + (-0.5x + 0.25x2) = 10 Combine like terms: 1.5x + -0.5x = 1x 1x + 0.25x2 = 10 Solving 1x + 0.25x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 1x + 0.25x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 1x + 0.25x2 = 0 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -40 + 4x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 4x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 4x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 4x + x2 = 0 + 40 4x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 4x + x2 = 40 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 40 + 4 Reorder the terms: 4 + 4x + x2 = 40 + 4 Combine like terms: 40 + 4 = 44 4 + 4x + x2 = 44 Factor a perfect square on the left side: (x + 2)(x + 2) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (x + 2) equal to 6.633249581 and -6.633249581.Subproblem 1
x + 2 = 6.633249581 Simplifying x + 2 = 6.633249581 Reorder the terms: 2 + x = 6.633249581 Solving 2 + x = 6.633249581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 6.633249581 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.633249581 + -2 x = 6.633249581 + -2 Combine like terms: 6.633249581 + -2 = 4.633249581 x = 4.633249581 Simplifying x = 4.633249581Subproblem 2
x + 2 = -6.633249581 Simplifying x + 2 = -6.633249581 Reorder the terms: 2 + x = -6.633249581 Solving 2 + x = -6.633249581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -6.633249581 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.633249581 + -2 x = -6.633249581 + -2 Combine like terms: -6.633249581 + -2 = -8.633249581 x = -8.633249581 Simplifying x = -8.633249581Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.633249581, -8.633249581}
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