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Simplifying 10x2 + 29x + -15 = 0 Reorder the terms: -15 + 29x + 10x2 = 0 Solving -15 + 29x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.5 + 2.9x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 2.9x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 2.9x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 2.9x + x2 = 0 + 1.5 2.9x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 2.9x + x2 = 1.5 The x term is 2.9x. Take half its coefficient (1.45). Square it (2.1025) and add it to both sides. Add '2.1025' to each side of the equation. 2.9x + 2.1025 + x2 = 1.5 + 2.1025 Reorder the terms: 2.1025 + 2.9x + x2 = 1.5 + 2.1025 Combine like terms: 1.5 + 2.1025 = 3.6025 2.1025 + 2.9x + x2 = 3.6025 Factor a perfect square on the left side: (x + 1.45)(x + 1.45) = 3.6025 Calculate the square root of the right side: 1.89802529 Break this problem into two subproblems by setting (x + 1.45) equal to 1.89802529 and -1.89802529.Subproblem 1
x + 1.45 = 1.89802529 Simplifying x + 1.45 = 1.89802529 Reorder the terms: 1.45 + x = 1.89802529 Solving 1.45 + x = 1.89802529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.45' to each side of the equation. 1.45 + -1.45 + x = 1.89802529 + -1.45 Combine like terms: 1.45 + -1.45 = 0.00 0.00 + x = 1.89802529 + -1.45 x = 1.89802529 + -1.45 Combine like terms: 1.89802529 + -1.45 = 0.44802529 x = 0.44802529 Simplifying x = 0.44802529Subproblem 2
x + 1.45 = -1.89802529 Simplifying x + 1.45 = -1.89802529 Reorder the terms: 1.45 + x = -1.89802529 Solving 1.45 + x = -1.89802529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.45' to each side of the equation. 1.45 + -1.45 + x = -1.89802529 + -1.45 Combine like terms: 1.45 + -1.45 = 0.00 0.00 + x = -1.89802529 + -1.45 x = -1.89802529 + -1.45 Combine like terms: -1.89802529 + -1.45 = -3.34802529 x = -3.34802529 Simplifying x = -3.34802529Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.44802529, -3.34802529}
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