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Simplifying 100 = 28x2 + 12x Reorder the terms: 100 = 12x + 28x2 Solving 100 = 12x + 28x2 Solving for variable 'x'. Reorder the terms: 100 + -12x + -28x2 = 12x + -12x + 28x2 + -28x2 Combine like terms: 12x + -12x = 0 100 + -12x + -28x2 = 0 + 28x2 + -28x2 100 + -12x + -28x2 = 28x2 + -28x2 Combine like terms: 28x2 + -28x2 = 0 100 + -12x + -28x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(25 + -3x + -7x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(25 + -3x + -7x2)' equal to zero and attempt to solve: Simplifying 25 + -3x + -7x2 = 0 Solving 25 + -3x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -3.571428571 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '3.571428571' to each side of the equation. -3.571428571 + 0.4285714286x + 3.571428571 + x2 = 0 + 3.571428571 Reorder the terms: -3.571428571 + 3.571428571 + 0.4285714286x + x2 = 0 + 3.571428571 Combine like terms: -3.571428571 + 3.571428571 = 0.000000000 0.000000000 + 0.4285714286x + x2 = 0 + 3.571428571 0.4285714286x + x2 = 0 + 3.571428571 Combine like terms: 0 + 3.571428571 = 3.571428571 0.4285714286x + x2 = 3.571428571 The x term is 0.4285714286x. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x + 0.04591836735 + x2 = 3.571428571 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 3.571428571 + 0.04591836735 Combine like terms: 3.571428571 + 0.04591836735 = 3.61734693835 0.04591836735 + 0.4285714286x + x2 = 3.61734693835 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 3.61734693835 Calculate the square root of the right side: 1.901932422 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 1.901932422 and -1.901932422.Subproblem 1
x + 0.2142857143 = 1.901932422 Simplifying x + 0.2142857143 = 1.901932422 Reorder the terms: 0.2142857143 + x = 1.901932422 Solving 0.2142857143 + x = 1.901932422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = 1.901932422 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 1.901932422 + -0.2142857143 x = 1.901932422 + -0.2142857143 Combine like terms: 1.901932422 + -0.2142857143 = 1.6876467077 x = 1.6876467077 Simplifying x = 1.6876467077Subproblem 2
x + 0.2142857143 = -1.901932422 Simplifying x + 0.2142857143 = -1.901932422 Reorder the terms: 0.2142857143 + x = -1.901932422 Solving 0.2142857143 + x = -1.901932422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = -1.901932422 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -1.901932422 + -0.2142857143 x = -1.901932422 + -0.2142857143 Combine like terms: -1.901932422 + -0.2142857143 = -2.1162181363 x = -2.1162181363 Simplifying x = -2.1162181363Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6876467077, -2.1162181363}Solution
x = {1.6876467077, -2.1162181363}
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