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Simplifying 10x2 + -19 = -8x Reorder the terms: -19 + 10x2 = -8x Solving -19 + 10x2 = -8x Solving for variable 'x'. Reorder the terms: -19 + 8x + 10x2 = -8x + 8x Combine like terms: -8x + 8x = 0 -19 + 8x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.9 + 0.8x + x2 = 0 Move the constant term to the right: Add '1.9' to each side of the equation. -1.9 + 0.8x + 1.9 + x2 = 0 + 1.9 Reorder the terms: -1.9 + 1.9 + 0.8x + x2 = 0 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + 0.8x + x2 = 0 + 1.9 0.8x + x2 = 0 + 1.9 Combine like terms: 0 + 1.9 = 1.9 0.8x + x2 = 1.9 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 1.9 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 1.9 + 0.16 Combine like terms: 1.9 + 0.16 = 2.06 0.16 + 0.8x + x2 = 2.06 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 2.06 Calculate the square root of the right side: 1.435270009 Break this problem into two subproblems by setting (x + 0.4) equal to 1.435270009 and -1.435270009.Subproblem 1
x + 0.4 = 1.435270009 Simplifying x + 0.4 = 1.435270009 Reorder the terms: 0.4 + x = 1.435270009 Solving 0.4 + x = 1.435270009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 1.435270009 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.435270009 + -0.4 x = 1.435270009 + -0.4 Combine like terms: 1.435270009 + -0.4 = 1.035270009 x = 1.035270009 Simplifying x = 1.035270009Subproblem 2
x + 0.4 = -1.435270009 Simplifying x + 0.4 = -1.435270009 Reorder the terms: 0.4 + x = -1.435270009 Solving 0.4 + x = -1.435270009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -1.435270009 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.435270009 + -0.4 x = -1.435270009 + -0.4 Combine like terms: -1.435270009 + -0.4 = -1.835270009 x = -1.835270009 Simplifying x = -1.835270009Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.035270009, -1.835270009}
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