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Simplifying 23 + -7(x + 3) * 5x = 10 Reorder the terms: 23 + -7(3 + x) * 5x = 10 Reorder the terms for easier multiplication: 23 + -7 * 5x(3 + x) = 10 Multiply -7 * 5 23 + -35x(3 + x) = 10 23 + (3 * -35x + x * -35x) = 10 23 + (-105x + -35x2) = 10 Solving 23 + -105x + -35x2 = 10 Solving for variable 'x'. Reorder the terms: 23 + -10 + -105x + -35x2 = 10 + -10 Combine like terms: 23 + -10 = 13 13 + -105x + -35x2 = 10 + -10 Combine like terms: 10 + -10 = 0 13 + -105x + -35x2 = 0 Begin completing the square. Divide all terms by -35 the coefficient of the squared term: Divide each side by '-35'. -0.3714285714 + 3x + x2 = 0 Move the constant term to the right: Add '0.3714285714' to each side of the equation. -0.3714285714 + 3x + 0.3714285714 + x2 = 0 + 0.3714285714 Reorder the terms: -0.3714285714 + 0.3714285714 + 3x + x2 = 0 + 0.3714285714 Combine like terms: -0.3714285714 + 0.3714285714 = 0.0000000000 0.0000000000 + 3x + x2 = 0 + 0.3714285714 3x + x2 = 0 + 0.3714285714 Combine like terms: 0 + 0.3714285714 = 0.3714285714 3x + x2 = 0.3714285714 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 0.3714285714 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 0.3714285714 + 2.25 Combine like terms: 0.3714285714 + 2.25 = 2.6214285714 2.25 + 3x + x2 = 2.6214285714 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 2.6214285714 Calculate the square root of the right side: 1.619082633 Break this problem into two subproblems by setting (x + 1.5) equal to 1.619082633 and -1.619082633.Subproblem 1
x + 1.5 = 1.619082633 Simplifying x + 1.5 = 1.619082633 Reorder the terms: 1.5 + x = 1.619082633 Solving 1.5 + x = 1.619082633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.619082633 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.619082633 + -1.5 x = 1.619082633 + -1.5 Combine like terms: 1.619082633 + -1.5 = 0.119082633 x = 0.119082633 Simplifying x = 0.119082633Subproblem 2
x + 1.5 = -1.619082633 Simplifying x + 1.5 = -1.619082633 Reorder the terms: 1.5 + x = -1.619082633 Solving 1.5 + x = -1.619082633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.619082633 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.619082633 + -1.5 x = -1.619082633 + -1.5 Combine like terms: -1.619082633 + -1.5 = -3.119082633 x = -3.119082633 Simplifying x = -3.119082633Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.119082633, -3.119082633}
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