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Simplifying 10x2 + 20x + -45 = 8 Reorder the terms: -45 + 20x + 10x2 = 8 Solving -45 + 20x + 10x2 = 8 Solving for variable 'x'. Reorder the terms: -45 + -8 + 20x + 10x2 = 8 + -8 Combine like terms: -45 + -8 = -53 -53 + 20x + 10x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -53 + 20x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -5.3 + 2x + x2 = 0 Move the constant term to the right: Add '5.3' to each side of the equation. -5.3 + 2x + 5.3 + x2 = 0 + 5.3 Reorder the terms: -5.3 + 5.3 + 2x + x2 = 0 + 5.3 Combine like terms: -5.3 + 5.3 = 0.0 0.0 + 2x + x2 = 0 + 5.3 2x + x2 = 0 + 5.3 Combine like terms: 0 + 5.3 = 5.3 2x + x2 = 5.3 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 5.3 + 1 Reorder the terms: 1 + 2x + x2 = 5.3 + 1 Combine like terms: 5.3 + 1 = 6.3 1 + 2x + x2 = 6.3 Factor a perfect square on the left side: (x + 1)(x + 1) = 6.3 Calculate the square root of the right side: 2.50998008 Break this problem into two subproblems by setting (x + 1) equal to 2.50998008 and -2.50998008.Subproblem 1
x + 1 = 2.50998008 Simplifying x + 1 = 2.50998008 Reorder the terms: 1 + x = 2.50998008 Solving 1 + x = 2.50998008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.50998008 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.50998008 + -1 x = 2.50998008 + -1 Combine like terms: 2.50998008 + -1 = 1.50998008 x = 1.50998008 Simplifying x = 1.50998008Subproblem 2
x + 1 = -2.50998008 Simplifying x + 1 = -2.50998008 Reorder the terms: 1 + x = -2.50998008 Solving 1 + x = -2.50998008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.50998008 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.50998008 + -1 x = -2.50998008 + -1 Combine like terms: -2.50998008 + -1 = -3.50998008 x = -3.50998008 Simplifying x = -3.50998008Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.50998008, -3.50998008}
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