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Simplifying 9 = 15x2 + -63x Reorder the terms: 9 = -63x + 15x2 Solving 9 = -63x + 15x2 Solving for variable 'x'. Reorder the terms: 9 + 63x + -15x2 = -63x + 63x + 15x2 + -15x2 Combine like terms: -63x + 63x = 0 9 + 63x + -15x2 = 0 + 15x2 + -15x2 9 + 63x + -15x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 9 + 63x + -15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + 21x + -5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + 21x + -5x2)' equal to zero and attempt to solve: Simplifying 3 + 21x + -5x2 = 0 Solving 3 + 21x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.6 + -4.2x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -4.2x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -4.2x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -4.2x + x2 = 0 + 0.6 -4.2x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -4.2x + x2 = 0.6 The x term is -4.2x. Take half its coefficient (-2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. -4.2x + 4.41 + x2 = 0.6 + 4.41 Reorder the terms: 4.41 + -4.2x + x2 = 0.6 + 4.41 Combine like terms: 0.6 + 4.41 = 5.01 4.41 + -4.2x + x2 = 5.01 Factor a perfect square on the left side: (x + -2.1)(x + -2.1) = 5.01 Calculate the square root of the right side: 2.238302929 Break this problem into two subproblems by setting (x + -2.1) equal to 2.238302929 and -2.238302929.Subproblem 1
x + -2.1 = 2.238302929 Simplifying x + -2.1 = 2.238302929 Reorder the terms: -2.1 + x = 2.238302929 Solving -2.1 + x = 2.238302929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + x = 2.238302929 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + x = 2.238302929 + 2.1 x = 2.238302929 + 2.1 Combine like terms: 2.238302929 + 2.1 = 4.338302929 x = 4.338302929 Simplifying x = 4.338302929Subproblem 2
x + -2.1 = -2.238302929 Simplifying x + -2.1 = -2.238302929 Reorder the terms: -2.1 + x = -2.238302929 Solving -2.1 + x = -2.238302929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + x = -2.238302929 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + x = -2.238302929 + 2.1 x = -2.238302929 + 2.1 Combine like terms: -2.238302929 + 2.1 = -0.138302929 x = -0.138302929 Simplifying x = -0.138302929Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.338302929, -0.138302929}Solution
x = {4.338302929, -0.138302929}
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