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Simplifying 10x2 + -20x + -19 = -5 Reorder the terms: -19 + -20x + 10x2 = -5 Solving -19 + -20x + 10x2 = -5 Solving for variable 'x'. Reorder the terms: -19 + 5 + -20x + 10x2 = -5 + 5 Combine like terms: -19 + 5 = -14 -14 + -20x + 10x2 = -5 + 5 Combine like terms: -5 + 5 = 0 -14 + -20x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -10x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -10x + 5x2)' equal to zero and attempt to solve: Simplifying -7 + -10x + 5x2 = 0 Solving -7 + -10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -2x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -2x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -2x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -2x + x2 = 0 + 1.4 -2x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -2x + x2 = 1.4 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 = 1.4 + 1 Reorder the terms: 1 + -2x + x2 = 1.4 + 1 Combine like terms: 1.4 + 1 = 2.4 1 + -2x + x2 = 2.4 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.4 Calculate the square root of the right side: 1.549193338 Break this problem into two subproblems by setting (x + -1) equal to 1.549193338 and -1.549193338.Subproblem 1
x + -1 = 1.549193338 Simplifying x + -1 = 1.549193338 Reorder the terms: -1 + x = 1.549193338 Solving -1 + x = 1.549193338 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 = 1.549193338 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.549193338 + 1 x = 1.549193338 + 1 Combine like terms: 1.549193338 + 1 = 2.549193338 x = 2.549193338 Simplifying x = 2.549193338Subproblem 2
x + -1 = -1.549193338 Simplifying x + -1 = -1.549193338 Reorder the terms: -1 + x = -1.549193338 Solving -1 + x = -1.549193338 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 = -1.549193338 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.549193338 + 1 x = -1.549193338 + 1 Combine like terms: -1.549193338 + 1 = -0.549193338 x = -0.549193338 Simplifying x = -0.549193338Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.549193338, -0.549193338}Solution
x = {2.549193338, -0.549193338}
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