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Simplifying 10x2 + -8x + -16 = -3 Reorder the terms: -16 + -8x + 10x2 = -3 Solving -16 + -8x + 10x2 = -3 Solving for variable 'x'. Reorder the terms: -16 + 3 + -8x + 10x2 = -3 + 3 Combine like terms: -16 + 3 = -13 -13 + -8x + 10x2 = -3 + 3 Combine like terms: -3 + 3 = 0 -13 + -8x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.3 + -0.8x + x2 = 0 Move the constant term to the right: Add '1.3' to each side of the equation. -1.3 + -0.8x + 1.3 + x2 = 0 + 1.3 Reorder the terms: -1.3 + 1.3 + -0.8x + x2 = 0 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + -0.8x + x2 = 0 + 1.3 -0.8x + x2 = 0 + 1.3 Combine like terms: 0 + 1.3 = 1.3 -0.8x + x2 = 1.3 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 = 1.3 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 1.3 + 0.16 Combine like terms: 1.3 + 0.16 = 1.46 0.16 + -0.8x + x2 = 1.46 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 1.46 Calculate the square root of the right side: 1.208304597 Break this problem into two subproblems by setting (x + -0.4) equal to 1.208304597 and -1.208304597.Subproblem 1
x + -0.4 = 1.208304597 Simplifying x + -0.4 = 1.208304597 Reorder the terms: -0.4 + x = 1.208304597 Solving -0.4 + x = 1.208304597 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 = 1.208304597 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.208304597 + 0.4 x = 1.208304597 + 0.4 Combine like terms: 1.208304597 + 0.4 = 1.608304597 x = 1.608304597 Simplifying x = 1.608304597Subproblem 2
x + -0.4 = -1.208304597 Simplifying x + -0.4 = -1.208304597 Reorder the terms: -0.4 + x = -1.208304597 Solving -0.4 + x = -1.208304597 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 = -1.208304597 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.208304597 + 0.4 x = -1.208304597 + 0.4 Combine like terms: -1.208304597 + 0.4 = -0.808304597 x = -0.808304597 Simplifying x = -0.808304597Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.608304597, -0.808304597}
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