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Simplifying 5 = 15x2 + 42x Reorder the terms: 5 = 42x + 15x2 Solving 5 = 42x + 15x2 Solving for variable 'x'. Reorder the terms: 5 + -42x + -15x2 = 42x + -42x + 15x2 + -15x2 Combine like terms: 42x + -42x = 0 5 + -42x + -15x2 = 0 + 15x2 + -15x2 5 + -42x + -15x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 5 + -42x + -15x2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -0.3333333333 + 2.8x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 2.8x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 2.8x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 2.8x + x2 = 0 + 0.3333333333 2.8x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 2.8x + x2 = 0.3333333333 The x term is 2.8x. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8x + 1.96 + x2 = 0.3333333333 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = 0.3333333333 + 1.96 Combine like terms: 0.3333333333 + 1.96 = 2.2933333333 1.96 + 2.8x + x2 = 2.2933333333 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 2.2933333333 Calculate the square root of the right side: 1.514375559 Break this problem into two subproblems by setting (x + 1.4) equal to 1.514375559 and -1.514375559.Subproblem 1
x + 1.4 = 1.514375559 Simplifying x + 1.4 = 1.514375559 Reorder the terms: 1.4 + x = 1.514375559 Solving 1.4 + x = 1.514375559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 1.514375559 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 1.514375559 + -1.4 x = 1.514375559 + -1.4 Combine like terms: 1.514375559 + -1.4 = 0.114375559 x = 0.114375559 Simplifying x = 0.114375559Subproblem 2
x + 1.4 = -1.514375559 Simplifying x + 1.4 = -1.514375559 Reorder the terms: 1.4 + x = -1.514375559 Solving 1.4 + x = -1.514375559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -1.514375559 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -1.514375559 + -1.4 x = -1.514375559 + -1.4 Combine like terms: -1.514375559 + -1.4 = -2.914375559 x = -2.914375559 Simplifying x = -2.914375559Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.114375559, -2.914375559}
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