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Simplifying 25x2 + -30x + -10 = 0 Reorder the terms: -10 + -30x + 25x2 = 0 Solving -10 + -30x + 25x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-2 + -6x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + -6x + 5x2)' equal to zero and attempt to solve: Simplifying -2 + -6x + 5x2 = 0 Solving -2 + -6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -1.2x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -1.2x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -1.2x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -1.2x + x2 = 0 + 0.4 -1.2x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -1.2x + x2 = 0.4 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 0.4 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 0.4 + 0.36 Combine like terms: 0.4 + 0.36 = 0.76 0.36 + -1.2x + x2 = 0.76 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting (x + -0.6) equal to 0.871779789 and -0.871779789.Subproblem 1
x + -0.6 = 0.871779789 Simplifying x + -0.6 = 0.871779789 Reorder the terms: -0.6 + x = 0.871779789 Solving -0.6 + x = 0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.871779789 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.871779789 + 0.6 x = 0.871779789 + 0.6 Combine like terms: 0.871779789 + 0.6 = 1.471779789 x = 1.471779789 Simplifying x = 1.471779789Subproblem 2
x + -0.6 = -0.871779789 Simplifying x + -0.6 = -0.871779789 Reorder the terms: -0.6 + x = -0.871779789 Solving -0.6 + x = -0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -0.871779789 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.871779789 + 0.6 x = -0.871779789 + 0.6 Combine like terms: -0.871779789 + 0.6 = -0.271779789 x = -0.271779789 Simplifying x = -0.271779789Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.471779789, -0.271779789}Solution
x = {1.471779789, -0.271779789}
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