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Simplifying -5x3 + 7x2 + 10x = 0 Reorder the terms: 10x + 7x2 + -5x3 = 0 Solving 10x + 7x2 + -5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(10 + 7x + -5x2) = 0Subproblem 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 '(10 + 7x + -5x2)' equal to zero and attempt to solve: Simplifying 10 + 7x + -5x2 = 0 Solving 10 + 7x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2 + -1.4x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.4x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -1.4x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.4x + x2 = 0 + 2 -1.4x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.4x + x2 = 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 = 2 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 2 + 0.49 Combine like terms: 2 + 0.49 = 2.49 0.49 + -1.4x + x2 = 2.49 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 2.49 Calculate the square root of the right side: 1.577973384 Break this problem into two subproblems by setting (x + -0.7) equal to 1.577973384 and -1.577973384.Subproblem 1
x + -0.7 = 1.577973384 Simplifying x + -0.7 = 1.577973384 Reorder the terms: -0.7 + x = 1.577973384 Solving -0.7 + x = 1.577973384 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 = 1.577973384 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 1.577973384 + 0.7 x = 1.577973384 + 0.7 Combine like terms: 1.577973384 + 0.7 = 2.277973384 x = 2.277973384 Simplifying x = 2.277973384Subproblem 2
x + -0.7 = -1.577973384 Simplifying x + -0.7 = -1.577973384 Reorder the terms: -0.7 + x = -1.577973384 Solving -0.7 + x = -1.577973384 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 = -1.577973384 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -1.577973384 + 0.7 x = -1.577973384 + 0.7 Combine like terms: -1.577973384 + 0.7 = -0.877973384 x = -0.877973384 Simplifying x = -0.877973384Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.277973384, -0.877973384}Solution
x = {0, 2.277973384, -0.877973384}
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