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Simplifying 5x(2x + 3) + 4(x + -1) + -7x = 0 Reorder the terms: 5x(3 + 2x) + 4(x + -1) + -7x = 0 (3 * 5x + 2x * 5x) + 4(x + -1) + -7x = 0 (15x + 10x2) + 4(x + -1) + -7x = 0 Reorder the terms: 15x + 10x2 + 4(-1 + x) + -7x = 0 15x + 10x2 + (-1 * 4 + x * 4) + -7x = 0 15x + 10x2 + (-4 + 4x) + -7x = 0 Reorder the terms: -4 + 15x + 4x + -7x + 10x2 = 0 Combine like terms: 15x + 4x = 19x -4 + 19x + -7x + 10x2 = 0 Combine like terms: 19x + -7x = 12x -4 + 12x + 10x2 = 0 Solving -4 + 12x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 6x + 5x2) = 0 Ignore the factor 2.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 = 0.271779789 x = 0.271779789 Simplifying x = 0.271779789Subproblem 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 = -1.471779789 x = -1.471779789 Simplifying x = -1.471779789Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.271779789, -1.471779789}Solution
x = {0.271779789, -1.471779789}
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