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Simplifying (3x2)(5x2 + 7x + -10) = 0 Remove parenthesis around (3x2) 3x2(5x2 + 7x + -10) = 0 Reorder the terms: 3x2(-10 + 7x + 5x2) = 0 (-10 * 3x2 + 7x * 3x2 + 5x2 * 3x2) = 0 (-30x2 + 21x3 + 15x4) = 0 Solving -30x2 + 21x3 + 15x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(-10 + 7x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 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 = 0.877973384 x = 0.877973384 Simplifying x = 0.877973384Subproblem 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 = -2.277973384 x = -2.277973384 Simplifying x = -2.277973384Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.877973384, -2.277973384}Solution
x = {0, 0.877973384, -2.277973384}
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