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Simplifying 10x2 + 28x + 14 = 0 Reorder the terms: 14 + 28x + 10x2 = 0 Solving 14 + 28x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 14x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 14x + 5x2)' equal to zero and attempt to solve: Simplifying 7 + 14x + 5x2 = 0 Solving 7 + 14x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + 2.8x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 2.8x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + 2.8x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 2.8x + x2 = 0 + -1.4 2.8x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 2.8x + x2 = -1.4 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 = -1.4 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = -1.4 + 1.96 Combine like terms: -1.4 + 1.96 = 0.56 1.96 + 2.8x + x2 = 0.56 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 0.56 Calculate the square root of the right side: 0.748331477 Break this problem into two subproblems by setting (x + 1.4) equal to 0.748331477 and -0.748331477.Subproblem 1
x + 1.4 = 0.748331477 Simplifying x + 1.4 = 0.748331477 Reorder the terms: 1.4 + x = 0.748331477 Solving 1.4 + x = 0.748331477 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 = 0.748331477 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 0.748331477 + -1.4 x = 0.748331477 + -1.4 Combine like terms: 0.748331477 + -1.4 = -0.651668523 x = -0.651668523 Simplifying x = -0.651668523Subproblem 2
x + 1.4 = -0.748331477 Simplifying x + 1.4 = -0.748331477 Reorder the terms: 1.4 + x = -0.748331477 Solving 1.4 + x = -0.748331477 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 = -0.748331477 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -0.748331477 + -1.4 x = -0.748331477 + -1.4 Combine like terms: -0.748331477 + -1.4 = -2.148331477 x = -2.148331477 Simplifying x = -2.148331477Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.651668523, -2.148331477}Solution
x = {-0.651668523, -2.148331477}
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