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Simplifying -3x(2x * 2x + -1x + -7) = 0 Reorder the terms for easier multiplication: -3x(2 * 2x * x + -1x + -7) = 0 Multiply 2 * 2 -3x(4x * x + -1x + -7) = 0 Multiply x * x -3x(4x2 + -1x + -7) = 0 Reorder the terms: -3x(-7 + -1x + 4x2) = 0 (-7 * -3x + -1x * -3x + 4x2 * -3x) = 0 (21x + 3x2 + -12x3) = 0 Solving 21x + 3x2 + -12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(7 + x + -4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(7 + x + -4x2)' equal to zero and attempt to solve: Simplifying 7 + x + -4x2 = 0 Solving 7 + x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.75 + -0.25x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -0.25x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -0.25x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -0.25x + x2 = 0 + 1.75 -0.25x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -0.25x + x2 = 1.75 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.25x + 0.25 + x2 = 1.75 + 0.25 Reorder the terms: 0.25 + -0.25x + x2 = 1.75 + 0.25 Combine like terms: 1.75 + 0.25 = 2 0.25 + -0.25x + x2 = 2 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 0.5) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 0.5 = 1.414213562 Simplifying x + 0.5 = 1.414213562 Reorder the terms: 0.5 + x = 1.414213562 Solving 0.5 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.414213562 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.414213562 + -0.5 x = 1.414213562 + -0.5 Combine like terms: 1.414213562 + -0.5 = 0.914213562 x = 0.914213562 Simplifying x = 0.914213562Subproblem 2
x + 0.5 = -1.414213562 Simplifying x + 0.5 = -1.414213562 Reorder the terms: 0.5 + x = -1.414213562 Solving 0.5 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.414213562 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.414213562 + -0.5 x = -1.414213562 + -0.5 Combine like terms: -1.414213562 + -0.5 = -1.914213562 x = -1.914213562 Simplifying x = -1.914213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.914213562, -1.914213562}Solution
x = {0, 0.914213562, -1.914213562}
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