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Simplifying 10x2 + -14x + 49 = 81 Reorder the terms: 49 + -14x + 10x2 = 81 Solving 49 + -14x + 10x2 = 81 Solving for variable 'x'. Reorder the terms: 49 + -81 + -14x + 10x2 = 81 + -81 Combine like terms: 49 + -81 = -32 -32 + -14x + 10x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -32 + -14x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + -7x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + -7x + 5x2)' equal to zero and attempt to solve: Simplifying -16 + -7x + 5x2 = 0 Solving -16 + -7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.2 + -1.4x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + -1.4x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + -1.4x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + -1.4x + x2 = 0 + 3.2 -1.4x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 -1.4x + x2 = 3.2 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 3.2 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 3.2 + 0.49 Combine like terms: 3.2 + 0.49 = 3.69 0.49 + -1.4x + x2 = 3.69 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 3.69 Calculate the square root of the right side: 1.920937271 Break this problem into two subproblems by setting (x + -0.7) equal to 1.920937271 and -1.920937271.Subproblem 1
x + -0.7 = 1.920937271 Simplifying x + -0.7 = 1.920937271 Reorder the terms: -0.7 + x = 1.920937271 Solving -0.7 + x = 1.920937271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 1.920937271 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 1.920937271 + 0.7 x = 1.920937271 + 0.7 Combine like terms: 1.920937271 + 0.7 = 2.620937271 x = 2.620937271 Simplifying x = 2.620937271Subproblem 2
x + -0.7 = -1.920937271 Simplifying x + -0.7 = -1.920937271 Reorder the terms: -0.7 + x = -1.920937271 Solving -0.7 + x = -1.920937271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -1.920937271 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -1.920937271 + 0.7 x = -1.920937271 + 0.7 Combine like terms: -1.920937271 + 0.7 = -1.220937271 x = -1.220937271 Simplifying x = -1.220937271Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.620937271, -1.220937271}Solution
x = {2.620937271, -1.220937271}
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