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Simplifying 0 = 5x2 + 14x + 2 Reorder the terms: 0 = 2 + 14x + 5x2 Solving 0 = 2 + 14x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + -14x + -5x2 = 2 + 14x + 5x2 + -2 + -14x + -5x2 Reorder the terms: -2 + -14x + -5x2 = 2 + -2 + 14x + -14x + 5x2 + -5x2 Combine like terms: 2 + -2 = 0 -2 + -14x + -5x2 = 0 + 14x + -14x + 5x2 + -5x2 -2 + -14x + -5x2 = 14x + -14x + 5x2 + -5x2 Combine like terms: 14x + -14x = 0 -2 + -14x + -5x2 = 0 + 5x2 + -5x2 -2 + -14x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -2 + -14x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 14x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 14x + 5x2)' equal to zero and attempt to solve: Simplifying 2 + 14x + 5x2 = 0 Solving 2 + 14x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 2.8x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 2.8x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 2.8x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 2.8x + x2 = 0 + -0.4 2.8x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 2.8x + x2 = -0.4 The x term is 2.8x. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8x + 1.96 + x2 = -0.4 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = -0.4 + 1.96 Combine like terms: -0.4 + 1.96 = 1.56 1.96 + 2.8x + x2 = 1.56 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 1.56 Calculate the square root of the right side: 1.2489996 Break this problem into two subproblems by setting (x + 1.4) equal to 1.2489996 and -1.2489996.Subproblem 1
x + 1.4 = 1.2489996 Simplifying x + 1.4 = 1.2489996 Reorder the terms: 1.4 + x = 1.2489996 Solving 1.4 + x = 1.2489996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 1.2489996 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 1.2489996 + -1.4 x = 1.2489996 + -1.4 Combine like terms: 1.2489996 + -1.4 = -0.1510004 x = -0.1510004 Simplifying x = -0.1510004Subproblem 2
x + 1.4 = -1.2489996 Simplifying x + 1.4 = -1.2489996 Reorder the terms: 1.4 + x = -1.2489996 Solving 1.4 + x = -1.2489996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -1.2489996 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -1.2489996 + -1.4 x = -1.2489996 + -1.4 Combine like terms: -1.2489996 + -1.4 = -2.6489996 x = -2.6489996 Simplifying x = -2.6489996Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1510004, -2.6489996}Solution
x = {-0.1510004, -2.6489996}
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