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Simplifying 95x2 + 190x + -5 = 0 Reorder the terms: -5 + 190x + 95x2 = 0 Solving -5 + 190x + 95x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-1 + 38x + 19x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-1 + 38x + 19x2)' equal to zero and attempt to solve: Simplifying -1 + 38x + 19x2 = 0 Solving -1 + 38x + 19x2 = 0 Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -0.05263157895 + 2x + x2 = 0 Move the constant term to the right: Add '0.05263157895' to each side of the equation. -0.05263157895 + 2x + 0.05263157895 + x2 = 0 + 0.05263157895 Reorder the terms: -0.05263157895 + 0.05263157895 + 2x + x2 = 0 + 0.05263157895 Combine like terms: -0.05263157895 + 0.05263157895 = 0.00000000000 0.00000000000 + 2x + x2 = 0 + 0.05263157895 2x + x2 = 0 + 0.05263157895 Combine like terms: 0 + 0.05263157895 = 0.05263157895 2x + x2 = 0.05263157895 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 = 0.05263157895 + 1 Reorder the terms: 1 + 2x + x2 = 0.05263157895 + 1 Combine like terms: 0.05263157895 + 1 = 1.05263157895 1 + 2x + x2 = 1.05263157895 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.05263157895 Calculate the square root of the right side: 1.025978352 Break this problem into two subproblems by setting (x + 1) equal to 1.025978352 and -1.025978352.Subproblem 1
x + 1 = 1.025978352 Simplifying x + 1 = 1.025978352 Reorder the terms: 1 + x = 1.025978352 Solving 1 + x = 1.025978352 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 = 1.025978352 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.025978352 + -1 x = 1.025978352 + -1 Combine like terms: 1.025978352 + -1 = 0.025978352 x = 0.025978352 Simplifying x = 0.025978352Subproblem 2
x + 1 = -1.025978352 Simplifying x + 1 = -1.025978352 Reorder the terms: 1 + x = -1.025978352 Solving 1 + x = -1.025978352 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 = -1.025978352 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.025978352 + -1 x = -1.025978352 + -1 Combine like terms: -1.025978352 + -1 = -2.025978352 x = -2.025978352 Simplifying x = -2.025978352Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.025978352, -2.025978352}Solution
x = {0.025978352, -2.025978352}
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